 So, today I am going to talk about prediction of the monsoon, because billions of people around the world are interested in prediction of the monsoon. Now, monsoon prediction for most of the people in India implies prediction of the Indian summer monsoon rainfall ISMR, since the impact of the vagaries of ISMR on critical facets of our economies perceived to be very significant. However, we have seen that the Indian summer monsoon rainfall is one of the most reliable events in the tropical calendar. The standard deviation of the interannual variation of ISMR is only about 10 percent of the average rainfall of 85 centimeters. Now, the frequency distribution of ISMR is not symmetric. See, this is the frequency distribution. So, this shows what is the percentage of years in which the rainfall is around 85, around 87.5, around 90 and so on and so forth. And this is based on the data from 1876 to 2007. So, the frequency distribution is not symmetric and you can see that that you know it has a very long tail towards the lower rainfall region compared to the high rainfall region. High rainfall region is fairly sharp ending, but here there is a long tail. So, we say that it is not symmetric. It is characterized by a longer tail with negative anomalies than that with positive anomalies. Over the 132 year period, there have been 23 droughts and 19 excess rainfall years. Because historical records show that the chance of the so called normal monsoon, which means neither a drought nor an excess rainfall is a little over 68 percent, droughts around 17 percent and excess rainfall around 14 percent. So, this is just the chance based on historical data. While for the worst drought 1877, the ISMR deficit was as large as 25 centimeter. So, the season with maximum rainfall 1961 ISMR anomaly was 17 centimeter. It is seen that the most likely value of ISMR, the mode is around 90 centimeters. You can see here maximum chance occurs that is almost 20 percent when the rain is around 90 or so. So, the mode is around 90 centimeters that is higher than the average and that the rainfall in the range 83.75 to 91.25 that is to say 1.25 on either side of 85 is 44 percent of years. So, large number of years have rainfall rather close to the normal. Now, in the last lecture on monsoon GDP and agriculture, we have seen that although the amplitude of variation of ISMR from year to year is not large, it has a substantial impact on the agricultural production in the country and also the GDP. The impact of severe droughts on GDP remained between 2 to 5 percent of GDP from 1950 to 2003. So, while the magnitude of the adverse impact on food grain production and GDP of deficit rainfall is large, the positive impact of surplus rainfall is not large. So, this asymmetry in the response is particularly large after 1980. So, this is in fact the food grain production impact, impact on food grain production and this is ISMR anomalies and what you see here is that on the positive side the curve is rather flat on the negative side very sharp impact as you get more and more severe deficit and the same story is there also for GDP. This is for FGP and the last one is for GDP. It has been suggested that a possible reason for the relatively low response of food grain production to average and above average monsoon rainfall post 1980 is that strategies that would allow farmers to reap benefit of good rainfall years such as adequate investments in fertilizers and pesticides over in fed areas are not economically viable in the current milieu. So, why is the response asymmetric? It has been suggested that in the present current milieu the situation is such that even if the rainfall is good you cannot get good yields unless there is enough investment in fertilizers and pesticides and farmers are reluctant to make that investment because they do not know that is going to be a good rainfall year basically that is the problem. Such strategies would become economically viable if reliable predictions for no droughts could be generated. Thus prediction of the inter-annual variation of ISMR particularly for the occurrence or non-occurrence of the extremes that is droughts and excess rainfall season continues to be extremely important. Now, so there has been not surprisingly focus of the monsoon prediction has been on seasonal prediction prediction of the seasonal rainfall. Now, in addition to prediction of the monsoon rainfall over the country as a whole there is a demand for prediction of some events such as the intense rainfall event on 26 July 2005 when Mumbai received 94.4 centimetres of rainfall on a single day or of the severe cyclone that devastated Orissa in 1999 because of the enormous impact they have on a large number of people. So, these are predictions on a much shorter time scale for an event which is also of much shorter time scale. These are also in demand there is also a need for several user specific predictions such as prediction of low level winds for sailors and for paragliding enthusiasts, quantitative precipitation forecast for reservoir and flood management and so on. The time scales of the events for which prediction is required also varies with the application. Thus, while some farmers need prediction for occurrence of a dry spell of duration of a week or more for managers of reservoirs prediction of the total rainfall in a month or a season is often adequate. In these two lectures I shall give some background on meteorological forecasts and predictability. It will not be possible to do justice to this important topic of monsoon predictions in two lectures. So, after mentioning an example of short range forecast I shall focus on the long range prediction of seasonal rainfall averaged over the Indian region that is ISMR with statistical models and state of the art climate models which are models of the coupled ocean atmosphere system based on laws of physics. So, I have to in fact omit many topics which would be of interest simply because this is too large a topic to be covered in two lectures. So, I must mention that although it has not been possible to devote any time in this lecture series to atmospheric and climate models our understanding of the nature of the inter annual variation of ISMR including recent advances has been discussed in some detail here. So, it is now possible to discuss in some depth the present skill of prediction of the inter annual variation of ISMR with the state of art climate models and particularly prediction of extremes because we know that is more important prediction of extremes that is to say droughts and excess rainfall season. So, with this then this kind of analysis of how good the climate models are in predicting inter annual variation of ISMR suggests important milestones that have to be crossed in the endeavor to improve the models to give satisfactory predictions of the monsoon. Now, so let us begin at the beginning what are meteorological forecasts. Meteorological forecasts are generated for different time scales. So, forecasts of daily weather with a lead time of 1 to 3 days are called short range forecast and with a lead time of 3 to 10 days are called medium range forecast. Reports for monthly or seasonal rainfall come under the category of long range forecast. So, depending on the time scale we have forecast which are short range, medium range and long range. India meteorological department IMD is the agency responsible for generating forecasts on all these time scales in our country. But I must also mention that there is a centre national centre for medium range weather forecasting which does a lot of research on models which can generate forecasts on the medium range. Also at present efforts are being made the world over to generate predictions over an intermediate time scale the so called extended range prediction with a lead time of 10 days to a month. So, this is between medium range and long range for rainfall temperature etcetera. In fact, such extended range predictions have been made by IITM scientist from 2011 that is for the past 2 years and going on for this year as well on an experimental basis. Now, space and time scales are inexorably linked. So, while short range forecasts are generated for the meteorological subdivisions of India which are given here these are the meteorological subdivisions of India and even smaller spatial scales such as the strict level and so on long range forecasts are made for larger regions such as the all India scale or 3 or 4 subdivisions of the country. So, this is for the short range and for long range these are the zones over which India made department generates forecasts in addition to the all India scale. Now, how do meteorologists generate forecasts? Scientists and laymen often find it difficult to understand the reasons for the painfully slow progress in forecasting the weather and climate in the modern day milieu of satellites and computers. When solar eclipses can be predicted to fractions of a second and the position of a satellite been pointed millions of miles out in space why cannot reliable weather predictions be made for a day, a week, a month, season or years in advance. See, this is a question that is often posed by laymen to meteorologists. In fact, the problem of generating predictions of meteorological events such as heavy rainfall over a region is more complex than that of generating predictions of planetary orbits. This is because the atmosphere is unstable and the systems responsible for the events that we are trying to predict such as clouds or a monsoon depression in which thousands of clouds are embedded are the culmination of the instabilities of the atmosphere. We have actually seen this in this course how the systems that are responsible for a rainfall are actually culmination of instabilities of the atmosphere. So, by its very nature these systems are different from the stable systems which characterize planetary orbits. Now, we have seen that they involve non-linear interaction between different spatial scales from 3 to 4 kilometers as in a single cloud to 100s of kilometers as in a monsoon depression or hurricane. So, this is what makes the problem of weather or climate prediction inherently more complicated than that of prediction of planetary orbits. Let us first try to understand how predictions are generated. The state of the atmosphere at any point of time in terms of temperature, wind, rainfall etcetera as a function of space evolves according to Newton's laws as applied to a compressible fluid in a rotating system. Hence, the logical way of predicting the future scale of atmosphere, future state of the atmosphere say 24 or 48 hours is to integrate the governing equations starting with the observed state of the atmosphere at the initial instant as the initial condition and the observed conditions at the surface of land or ocean as the boundary condition for 24 or 48 hours as required. So, this is the logical way we have laws which tell you how things will change with time. So, you start with an initial condition from observation and integrate those equations governing equations derived from the laws to tell you what the next state would be say 24 hours or 48 hours ahead which may come after several time steps in the numerical integration of course. Now, some errors in the short range forecast occur because the models are not perfect. You know the models involve many assumptions such as about how the sub grid scale processes like clouds affect the heating. See the typical grid size of a model is of the order of 100 kilometers although now much higher resolution models are being developed whereas the cloud scale is a few kilometers. So, cloud is necessarily a sub grid scale phenomena and how to incorporate the effects of clouds in terms of spatial variables which vary over the grid scale is a very important problem. This is what is called parametrization and these parametrizations involve many assumptions which means that the models are not perfect in this respect. Also, there are large errors and gaps in the observations of the initial state. So, first of all the models are not perfect. Secondly, the observations are not perfect in giving the kind of initial condition that is demanded. So, these are two elements that cause errors but there is even a more fundamental element that comes in and Lorenz was the first to elucidate this and this is the predictability of the atmosphere. See an important question is even with a perfect model and high resolution observations can we predict a week, month or a season ahead the weather at a particular place at a specific instant namely the state of the atmosphere at that instant at that point in space. So, even with a perfect model can we predict say a certain time period ahead say week or month or season the weather at a particular place say Bangalore at a specific instant namely this implies that can we actually say what the state of the atmosphere would be at a specific instant at a specific point in space. In fact, even with a perfect model it will never be a possible to predict weather more than about 7 days ahead. So, there is an inherent limit to predictability of weather and this is because there is an inherent limit to predictability of weather in a pioneering study Lorenz showed that if we start integrating the governing equations from two very similar initial conditions that is to say we take an initial condition and take a second initial condition which is only very little different from the other in the phase space of the meteorological variables. So, if we start with very very similar states if the system was stable then the solutions would stay close throughout however in the atmosphere not being stable when we start from two very similar initial conditions as they evolve because of the instabilities of the atmosphere where those two solutions start diverging with time. So, they go on going further and further apart with time and the difference in the predicted states increases with time. So, this is what is called you know sensitive dependence on initial conditions which is a property of the atmosphere which arises due to the presence of instabilities. By about 7 days the initial condition appears to be forgotten the difference between the two states then becomes comparable to the difference between two states evolving from two randomly chosen initial condition. So, what is happening is by about 7 days the atmosphere does not remember the initial condition at all and Lorenz's study introduced the concept of chaos and the atmosphere became the first known example of a chaotic system. So, this is what happens in a chaotic system the two states which are initially close become after a period of time in the case of the atmosphere about 7 days as far apart as states which have evolved from two random initial conditions which are not at all close. So, this is the chaos that you see in the atmosphere. So, there is an inherent limit of prediction of the atmosphere therefore, you can never ask for say rainfall at Bangalore on 16th of July 2014 it is a foolish question to ask because it is way beyond the limits of predictability. But what you can ask is something else prediction of monthly and seasonal mean. So, although weather is inherently unpredictable beyond about a week fortunately every facet of the atmosphere is not chaotic on all time scales. In fact, variation of climatic elements averaged over regions of different spatial and temporal scale example interannual variation of seasonal rainfall over the Indian region. So, here is rainfall averaged over a fairly large scale region the Indian region and over time as well from June to September. Now, the variation of this beast which we are interested in ISMR arises partly from variation of condition at the lower boundary of the atmosphere such as the sea surface temperature or snow cover over Eurasia. So, part of the variation is actually driven by boundary forcing sea surface temperature when the atmosphere is over the ocean or conditions like snow cover over Eurasia or land surface conditions over other parts of land. Hence, such variables can be used as predictors for this time scales thus a seasonal forecasting is primarily a boundary value problem although even while doing seasonal forecasting with models some initial conditions have to be specified. But the signal comes from the boundary forcing when it comes to seasonal scale. So, seasonal scale forecasting is a boundary value problem while short or medium range weather forecasting is primarily an initial value problem extended range prediction is between and it will depend on initial as well as boundary conditions. So, this is the general introduction to forecast now let me give an example of short range forecast. See, the first short range forecast were made by meteorologists with empirical knowledge of how weather maps evolved from day to day. So, in the old days before we started having numerical models to integrate and give us the state of the atmosphere which is predicted from the initial conditions what meteorologists had were weather maps and they knew by looking at a whole series of weather maps how systems on the weather maps evolved and this empirical knowledge was translated into methods for prediction. So, by the 50s development of physical models of the atmosphere on the one hand and detailed observations of the system on the other led to insights into physics of the variation on the scale of a few days. So, initially it was a naturalist understanding of how weather charts evolved and then we had development of physical models and detailed observations which gave insight into the critical physics of the important weather phenomena. So, with the advent of satellites and computers the density of observations increased enormously and complex models of the atmosphere that could simulate the short and medium range variation realistically were developed by the 1980s. Now, the integration of such models with initial conditions obtained from the worldwide observation network is a major input for weather prediction on these time scales. In India atmospheric and climate models are run regularly for this purpose at IMDA and the National Centre for Medium Range Weather Forecasting in CMRWF. Since 2011 as I mentioned before extended range forecast have been generated with such models by the Indian Institute of Tropical Meteorology IITM. Now predictions on the seasonal to interest annual scale there are two ways by which these predictions can be made. Such predictions can be generated by using ensemble of runs couple of couple models in which oceans also evolve with varying initial conditions. It is also possible to generate such predictions with atmospheric models and why is that because the oceans evolve more slowly than the atmosphere. So, the conditions at the surface of the ocean can be specified and atmospheric models can be run to get a prediction of the atmospheric conditions on the seasonal scale. For predictions with atmospheric models the boundary conditions particularly the SST sea surface temperature have to be predicted. Now there have been several studies of the performance of atmospheric models in the simulation of inter-annual variation by running them for several years with observed SST specified as the boundary condition. So, what has been done is to actually specify the observed SST for a set of years which are of obviously past years several years and run the atmospheric model. This was first done under an international project atmospheric model into comparison project IMIP. This is supposed to assess the maximum skill attainable in an atmospheric model. For long range predictions an alternative approach is the traditional one in which statistical models are used for prediction. Just like in the earlier short range predictions also a statistical models based on empirical knowledge of how weather charts evolve were used. Now for long range prediction an alternative approach is one in which statistical models are used for prediction. So what are these models based on these models are based on the links of the predictant what we want to predict in this case rainfall with prior values of that variable in other words with prior values of rainfall and or other variables such as pressure temperature of the atmosphere or ocean etcetera over the same or different regions of the atmosphere ocean discovered by analysis of a large number of data sets. So this involves looking at a large number of data sets and trying to discern links with some quantities prior to what we want to predict. Now so this is the general background of short range and long range forecast. Now let me give an example only one example of a short range forecast and this is the event on 26 27 July in 2005 in Mumbai when it received unprecedented heavy rainfall with its above Santa Cruz recording 94.4 centimeter of rainfall in 24 hours and there were reports of even heavier rainfall of 104.5 centimeters near Vihar lake. So this was a very intense rainfall event it disrupted life in the metropolis and caused a large number of deaths. The intensity of this event was not predicted either by IMD or by other operational forecast generated by major weather prediction groups like UK Met Office US Weather Service and so on. So none of them really predicted the intensity of this event. IMD's prediction made 24 hours ahead suggested a high probability of heavy rainfall, rainfall exceeding 12.5 centimeters over the region. However while the rainfall at Mumbai exceeding 12.5 centimeter in a day is a very common event in the rainy season rainfall over 90 centimeters in a day had never been experienced before. So certainly they did predict that they will be heavy rain but they could not at all a sense predict the actual intensity of the rain event that occurred. Had the prediction been more specific in terms of the probable intensity the damage could have been reduced to some extent and a number of lives could have been saved. Now a post facto analysis of the prediction of the Mumbai event suggests that it would have been possible to predict this event with high resolution atmospheric models. So this means with the grid size which is smaller than the usual 2.5 degree which is 250 kilometers or 100 kilometer. Much smaller grid that is high resolution atmospheric model provided high resolution data on clouds particularly on clouds organized over meso scale and larger scale available from satellite and quality control local meteorological data was used in specifying the initial condition. So both are important see the initial condition has to be accurately specified particularly in terms of the clouds and cloud systems that occur in the initial condition and that satellites is the only way one can get high resolution input on that and high resolution as well as over a large spatial scale. And the second is to run the models also with high resolution. So with both those were if both those were there then one could get the rain and this is just an example you can see yellows and greens mean not very high rain 2 centimeters and 4 centimeters and so on. And this is the NCMRWF model this is the UK Met Office model UK Met Office is at least getting good rain but it is still of the order of only 12 or 14 centimeters over Mumbai. JMA is also getting rain but more spread out and NCEP is not getting much of rain over west coast and neither is ECMWF however if we now actually specify the initial conditions properly and run a high resolution model then a peak value of about 80 centimeter can be predicted. So 80 centimeter is pretty close to 90 centimeter so had the forecast been made for this one would have been much better prepared. So what this tells us is that if we want to predict events of this kind in advance in a reliable manner it is essential to assimilate satellite data of high resolution into the initial condition and also essential to run models with very high resolution which take into account the topography also in a high resolution grid because you know near the western guards topography also plays an important role in the dynamics. Once the system which can assimilate the relevant data from Doppler radars from satellites high density meteorological observations in the metropolis as well as high resolution data on the terrain and land surface conditions is in place should be possible to generate reliable predictions of such events using the high resolution models available in the country. So this is in a way post factor analysis which leads to optimism that we should be able to harness our resources and generate reasonable predictions of intense rainfall events. Now let us consider long range predictions and in this lecture I will only consider the statistical models in the next lecture I will discuss how the climate models are the state of art coupled atmosphere ocean model systems perform in prediction of the monsoon. So forecasting of monsoon rainfall actually has a very long history over India it has been attempted for over 100 years in 1871 the Madras famine commission recommended that so far as it may be possible with the advance of knowledge to form a forecast of the future such it should be made use of though with due caution this is the comment from Madras famine commission and a major drought and famine occurred in India in 1877 and soon after that the India meteorological department was established. The first long range prediction in the world was made in 1886 by Blanford whose pioneering contributions to our understanding of monsoons we have already discussed in the earlier lectures but even in terms of predictions he was the first to make a prediction who Blanford who was the chief reporter of IMD at the request of the colonial government in the wake of this drought the prediction was based on the relationship between Himalayan snow cover and monsoon rainfall discovered by Blanford in 1884. So Blanford had found that the snow cover in over Himalaya if it is in excess in winter then the monsoon will be weaker and this relationship was used by him to predict. Now IMD has always been the responsible agency for operational long range forecast of monsoon rainfall which until recently have been based only on empirical models such as Blanford. Forecast during the initial years was subjective and qualitative. In the early part of the last century Sir Gilbert Walker whom we have met earlier when we discussed of course the El Nino and Southern Oscillation as well as of course Walker's Oscillation over the Pacific which was so named by Berkness. So Sir Gilbert Walker who has become more famous for these for the most exciting phenomena in tropics perhaps and so actually initiated extensive studies of the worldwide variation of weather elements pressure, temperature etc to develop models for monsoon prediction. In 1909 Walker introduced an objective technique based on correlation and regression analysis. The first model used by Walker in 1909 for prediction of ISMR was a linear regression model based on four predictors and you can see how much data they looked at to discover these predictors because it was based on Himalayan snow accumulation at the end of May on South American pressure during March to May, Mauritius pressure and Zanzibar rain in April and May. So amongst all this rainfall and pressure and variations and snow variation that he looked at he found these four variables are related to the subsequent monsoon and he actually predicted using that model. However, assessment of the predictions by this model by Montgomery up to 1936 showed that in spite of its early encouraging performance the formula had broken down completely in the 15 years from 1921. In the early 20s recognizing that the Indian region is not homogeneous with coherent variation of rainfall and hence too large to be considered as a unit Walker identified homogeneous regions called Northwest India and Peninsula on the basis of correlation with the predictors used. So he did it in a very logical way suppose you are using a predictor say the southern oscillation index then you correlate that southern oscillation index with rainfall over the region and then you if you find that this region has a correlation of a certain kind and this region has correlation of a different kind then these regions can be considered as homogeneous with respect to correlation with the predictor. So that is how he defined these homogeneous regions and he then developed models for predicting rainfall separately for these regions from 1924 to 87 forecast were issued only for these two regions. So only for these two regions of course the name is a bit peculiar because he calls this region which is sort of northern part of peninsula as peninsula leaving the southern peninsula totally out of it and Northwest India including Jammu Kashmir is called Northwest India these were walkers regions though. After the discovery of strong links between El Nino and Indian monsoon in the 80s with work by Sikkar, Asmose and Carpenter and so on the empirical models for monsoon prediction have developed very rapidly which is not surprising. In the tradition of walker a large number of potential predictors have been identified by analysis of the ever increasing data from conventional and satellite observations on many atmospheric and oceanic variables and they lack correlation with the monsoon rainfall over the Indian region. Some of these parameters are related to El Nino and southern oscillation others to snow over Himalayas and Eurasia and some to global and regional conditions on spatial scales ranging from one station for example surface temperature debilt in Holland to hemispheric example northern hemispheric surface air temperature in January and February. So whole variety of parameters had been identified. In fact as the sample of years increased with time the correlation coefficient with several parameters became poor and for some of them even change sign. Hence many revisions were made on the model by changing the predictors. So it was an ongoing process all the time the models were being updated and as the correlations became poor the predictors were dropped and new predictors were added and so on and so forth. It is important to note that during 32 to 87 although the quantitative predictions have been generated from the operational model for every year the forecast issued were often in terms of expected range or even more qualitative. Now this is a matter of political decision and in fact nowadays what we get are quantitative forecast or what is issued by IMD. But in the earlier era people were very careful not to give quantitative predictions. In order to assess the performance of the empirical models rather than the forecast issued in this paper Gargillian et al compared the predictions generated for the seasonal rainfall of northwest India and peninsula during 32 to 87 from the models used operational by IMD with observed rainfall. So now what you see here is for the three regions this is the peninsula which you have seen and this is predicted rainfall and this is observed rainfall. Then northwest India predicted rainfall observed rainfall and for all India predicted rainfall and observed rainfall. But this all India is only from 88 to 2004 this is by a new model introduced by IMD which I will come to but this is all the earlier models empirical models which are basically linear regression models. So if the predictions were perfect they should have been along this line here because predicted should have been equal to observed but what you see is a cloud of points here. First of the time you can see predictions are around 85, 90 or so and again for northwest India also it is not at all impressive okay there seem to be very large errors. So the mean of the predicted and observed June to September rainfall is comparable 56 and 54 respectively for northwest India and 87 and 89 centimeters respectively for peninsula. So the means of the predicted and observed came close to it however the standard deviation of predictions is much smaller than that of observations for northwest and peninsula. And see now this is the IMD rainfall and you can see how bad it is the correlation is only 0.25 is really a cloud here I mean there is no way by which the observe low observed rainfall has never been predicted high observed rainfall has been predicted only once here okay. The variation of the predicted rainfall for each season with the observed all India rainfall for this shows that the predictions are generally closer to the average than the observed values. Now what you see here is the error okay this is the error in the predictions and this is the observed rainfall okay. So the observed anomaly will be what the observed anomaly will be which is the mean minus observed okay so in any year the rainfall is given then mean minus observed is the observed anomaly of that year the negative of the observed anomaly of that year. So what you have that straight line that you see here is the mean minus observed and the points are predicted minus observed which is the error right and what is very interesting is that these points are falling very much along around this line see the line almost looks like a good linear fit to the cloud of points. So this is very interesting the points are scattered around the line and what does that line represent the variation of the error for each season with the observed rainfall is shown in the last slide note that if the predictions were always for rainfall equal to the average rainfall then the error would be negative of the anomaly of the observed rainfall right because if the predictions were always for the mean right then the mean minus observed would be the error and mean minus observed is just the negative observed anomaly right. So if the predictions were always for the rainfall equal to the average rainfall then the error would be negative of the anomaly of the observed and the line in each of the figures in the just represents this situation. So it is seen that the predictions are randomly scattered about this line so by and large the predictions are predictions for mean rainfall with the additional stochastic component around that from 88 to 2002 IMD reverted to issuing a forecast for the country as a whole including North East region instead of forecast for walkers to homogeneous regions of India. In 88 IMD introduced the 16 parameter power regression parametric models which were used operationally during 88 to 2002. Now how did they do? So what you see here is rainfall and this is the observation and this is the prediction and this is the magnitude of the error and you can see that errors are very very large at some points 94 the error is very large and so it is in 2002. So in fact errors are very large even though they made the model extremely complicated by going to power regression and so on and so forth. And this is the same actual and forecast you can see that there is a huge gap on several occasions between what is predicted and what is observed. Now consider next the extent to which the models are at least able to predict the sign of the anomaly we define seasons with rainfall below or above the average by more than one standard deviation as droughts or excess rainfall season. So as we do for ISMR for these regions also peninsula and northwest region of walker we define seasons with rainfall below the average by more than one standard deviation as drought above the average by more than one standard deviation from the mean as excess rainfall season of the 13 droughts that occurred over the peninsula only in 4 the predicted rainfall was deficit. So even the sign was predicted the sign was predicted correctly in the case of drought only in 4 out of 13 cases ok and of the 10 excess rainfall years that occurred also only in 4 cases the sign was positive anomaly predicted anomaly was positive while of the 8 droughts that occurred over northwest India only 7 the predicted was deficit. So this is not too bad but out of 10 excess only 3 the sign was right. So on the whole it is not able to capture the sign even the sign of the extremes and so the association coefficient which is the Pearson product moment correlation coefficient for northwest India and peninsula and also for all India was statistically not significant suggesting that the empirical operational models could not even predict the sign of the anomaly accurately. The variation of the magnitude of the error with time showed that there has not been any improvement over the years in spite of the continuing attempts to revise the operational models based on rigorous and objective statistical methods. This Gargi-Daital's analysis of the prediction generated by the empirical models used operationally by 32 and 2002 suggests that the performance of these models based on the relationship of the monsoon rainfall to atmospheric and oceanic conditions over different parts of the globe has not been satisfactory. The forecast failure in 2002 prompted IMD to critically examine these two models and introduce several new models. Now since then actually there has been a flurry of activity led by a very good meteorologist who used to be in IMD called Rajivan and they have developed new statistical models based on modern techniques called ensemble multiple linear regression and projection pursuit regression techniques which use new methods of predictor selection and model development and in the ensemble method is of relying on a single model all possible models based on the combination on all the combination of predictors are considered. So, out of all the possible models best few models are selected based on their skill in predicting monsoon rainfall during a common period. Forecast is then generated from weighted average of the forecast from the selected models. So, using all these modern tools has certainly seems to have helped and the model performance was evaluated for the period 81 to 2004 by sliding the model training period with a window length of 23 years and the correlation of ISMR with the predictions of these models is very high. It is of the order of 0.78 to 0.88 explaining about 60 percent of the variance. So, we seem to have with all these modern techniques hit on models which are reasonable then there is another statistical model developed by Ayungar and Raghu Kanth. This model was trained by this is a statistical model which uses past rainfall data as the input and this model was trained using ISMR data for the period 1872 to 1990 and tested for 91 to 2002 and they showed that the correlation for that forecast period although it is not very long was 0.91. So, it seems like there is hope that statistical models will have which have high skill in prediction of the monsoon will be developed in the near future. Now, I have not had a chance to go into great detail of the new version of statistical models partly because the new methods themselves would require exposition of the background you know these are not standard linear regression kind of models and a lot of work is involved and it is only by harnessing intelligent methods and some of the methods such as those of Ayungar actually involve non-linearities in the prediction schemes. So, it is only because of that that there appears to have been a success. I forgot to mention that the methods developed by Rajeev and Etel in fact successfully predicted the drought of 2009 which none of the dynamical models that is to say coupled models of the ocean atmosphere system could predict. So, the recent large drought of 2009 could be predicted by these models which were only tested in the paper they published up to 2004. So, 2002 and 4 were droughts and so was 2009 and Rajeev and Etel's model has been able to predict an extreme which is a very good thing. Now, let me just so I will not talk very much more in details about the statistical model, but for people who are interested I have given the key references here. First of all, Lorenz one of the greatest meteorologists of the century is a pioneering study of chaos, predictability and chaos and the first paper on that is predictability of a flow which possesses many scales of motion this is in 1969. For prediction of the Mumbai intense rainfall event there is a paper by Bohra Etel these are all from NCMRWF National Centre for Medium Range Weather Forecasting and they have actually done a heavy rainfall episode over Mumbai 20th July 2005 assessment of numerical weather prediction guidance. So, this has the references to the modern models high school high resolution models which could predict it. Now, there are many papers written on long range prediction because long range prediction has a very long history of more than 100 years here. And what I have done here is given you some of the recent references which in turn have references to all the older papers as well. One of them I have already mentioned from which I showed you data on how the models did from 1932 onwards what were the errors like and so on. Then there is this paper by Rajeevan which talks of the new models Iyengar and Raghunath again of the new models and for the uninitiated a popular review of the Indian monsoon prediction is in Science Journal Resonance for in December 2008. Thank you.