 So, today I am going to continue talking about Mansun variability and agriculture. As pointed out, climate variability has a direct impact on the growth and development of crops, this we have looked at already, as well as an indirect impact via triggering of pest diseases and weeds. Now, crop models developed over the last few decades for the different crops such as rice, wheat, groundnuts, sorghum, etcetera incorporate only some facets of the direct impact of climate variability. Direct impact is to say, impact on growth and development of the crop. So, for example, while all the models incorporate the impact of radiation on growth and development of the plant, only a few such as the peanut grow model which we looked at in the last class for groundnut, incorporate the effects of moisture stress induced by dry spells which are so important under rainfed conditions. None of the crop models incorporate the indirect impact of climate variability on agricultural productivity. Now, you know that there is considerable rainfall, variation in rainfall from year to year in our study region, the mean Anandpur and the mean annual rainfall is 57 centimeter and the standard deviation is as high as 16 centimeter. There is also considerable variation in the rainfall within the season. So, for example, in 1973, most of the rain fell from mid-September to mid-November. Hardly any rain in July or August, some rain in June and May. On the other hand, you look at 75 when there was plenty of rain in August, some rain in July and it continued to rain in September, October. So, there is a lot of variation from year to year in the rainfall and in particular in the timing of wet spells such as these and timing and length of dry spells such as these. So, there is a lot of variation from year to year and this leads to a very large variation in yield of crops like groundnut which are rain fed crops. So, they are very sensitive to the rainfall of the region. So, this is the district yield for Anandpur region and you can say that it varies a great deal. The maximum is very seldom more than 1000, only twice 1200 and 1300 or so it has come. But low yields are also quite frequent and in particular we had mentioned before that yields below 500 imply that even the cost of cultivation is not met so it should be considered as a failure. Now, we have seen this before that generally the district yield is much less than the peanut grow yield. So, this is the peanut grow yield in solid and by and large particularly when the peanut grow is reasonable say about 1000 or so, district yield is less than the peanut grow yield and by a very big margin when the yields are high of peanut grow. So, this we have seen however, the yield at the agricultural stations is comparable to peanut grow yield. This we have seen that by and large peanut grow captures the variability of the yield at agricultural stations. So, the yields on the farmers fields and hence the district yield is less because generally farmers do not apply pesticides because they are not cost effective in poor rainfall years. We had also discussed this that the yields on the farmers fields are much less because they do not think investment in application of pesticides is cost effective because it is not cost effective in poor rainfall years and they do not know which will be reasonable rainfall years. So, this is why they do not apply it. So, we therefore, expect that a large part of the difference between peanut grow yields and district yield is due to incidence and infestation of pests and diseases. Now, this is the large part of the difference has to be due to that and this is the difference between the agricultural research stations for different crops and the farmers fields and as we have seen that particularly when the yields are high there is a large difference between the farmers field and the agricultural research stations which could also be looked at as the crop model yield and the district average yield. Now, what we have done is we have developed a heuristic model for this indirect impact of climate variability via these yield reducing factors. What are the yield reducing factors we are considering pests diseases and weeds and we are taking into we are incorporating in this model impact of events such as wet spells and dry spells on triggering of these pests and diseases. We all know that triggering of pests and diseases depends on weather events this is well known for example, when we make pickles and the weather becomes very humid it is more likely to develop fungus this is well known. So, it is the same kind of thing triggering of certain diseases and pests by weather events this is what we are looking at and it must be emphasized that the model I am going to talk about today is in fact, for a very specific crop namely rain fed grounded and the specific variety that they are cultivating TMV2 and also specific to the region Anandpur region which I have shown on the map here and it is a part of the semi arid part of the peninsula and it receives only 57 centimeters of rain. So, this model that we have developed is specifically for this, but obviously the model can be generalized for other crops and other regions as well. And this is published in a paper in current science in 1999 I will not talk about all the details of the model. So, if interested people can refer to the original paper. So, now we are looking at heuristic model for impact of the major pest and diseases. For this the first thing we need is timing of the land preparation operations and the sowing in any year how do we determine that given the rainfall pattern of the year. So, this we had determined and I talked about the soil moisture model simple hydrological model that we had used and the criteria that the farmers use for the land preparation operations had been incorporated and that is how we determined when the specific land preparation operations will take place. Now the triggering of pest diseases and weeds is also based on criteria based on the knowledge of the farmers as conditions about the soil moisture and or rainfall. So, farmers have a lot of knowledge about when certain pests and diseases incidence will be triggered and on the basis of that we have actually developed the criteria. Now with this model the losses incurred from incidence of pest diseases and weeds in any year for which rainfall data are available can be inferred. So, now first of all this timing of land preparation and so on given the rainfall pattern of any year say 1965 then when would the first plow have occurred, when would the second plow had occurred and so on and so forth can be determined by this table which I have discussed earlier and based on the criteria that the farmers use. So, we have put it in terms of soil moisture at a depth of at a top layer depth of 20 meters and accordingly the harrowing takes place plowing and harrowing and sowing takes place again depending on the criteria. Now since the input of this model for land preparation and sowing timing is from farmers knowledge it is also important to actually see if what we are getting is reasonable in terms of the actual sowing dates that were observed. Now because we are going to apply these conditions to ascertain whether an opportunity to plow harrow and so occur in any year and if so the plowing harrowing and sowing dates are determined using the same table. So, because we are going to use it for this it is important to check whether this model is working all right and what we did was to compare the sowing date at the agricultural research station with the sowing date that this model yielded and we found that by and large again the details are in the paper the sowing date at agricultural research station was within a few days of the sowing date as determined by this model. So, the way the criteria have put in seem reasonable only difference arose when at the agricultural station they did not show at the first opportunity, but the second one. So, here we have assumed as is practiced again in that region that farmers will show at the first opportunity in their sowing window which is already put in to the model. So, we are fairly confident that the sowing date that the model yields is reasonable and consistent with what the farmers would have actually got. So, one of the major pests of ground nut is leaf miner. Now, this major pest is actually what has happened is as I mentioned earlier you know when we had the evolution from the traditional cropping system to the present cropping system large tracts of land went under monocrop the same ground nut and same variety and further more very often the life history stages of the plant would also be same over vast regions because people would adopt the same sowing date and so on and so forth. So, with this what has happened is that many pests and diseases have become endemic you know this means that for example, if we look at the pest leaf miner always there is a small population of leaf miner present in these ground nut fields. So, there is always a small population present and when favorable climate conditions favorable for the leaf miner and adverse as far as the yield is concerned. So, when these favorable climate conditions occur then suddenly the population explodes and attacks the crop. So, in particular for leaf miner the favorable conditions are long dry spells which are characterized by high temperature and low humidity. So, when they occur the populations build up very rapidly and attack the plants. So, how do we define now when the leaf miner population is going to build up. So, what we do is we define dry conditions which can promote leaf miner growth in terms of the soil moisture. Soil moisture less than 50 percent of the maximum value is taken as a dry day. So, you have soil moisture less than 50 percent of the remember SA was the maximum value that is the total field capacity minus the wilting point. So, whenever the soil moisture is less than 50 percent of the maximum value we take that as a dry day and a leaf miner day is defined as one on which the soil is dry that is to say the soil moisture is less than 50 percent of the maximum and it is a non rainy day. So, we use the IMD definition of rainy day as a day with rainfall less than 0.25 millimeters. So, we use the IMD definition of a non rainy day as the one with rainfall less than 0.25 millimeters. If an intense shower occurs in the initial stages of the leaf miner attack and this again is based on observations in the field by the farmers that in the early stages when the population of leaf miner are building up. If there is an intense rain shower then the population of the pest decreases and the plant recovers from the moisture stress. We should remember that when we talk of leaf miner days not only is the is it favorable for the leaf miner to grow it is also unfavorable for the crop to grow because of the moisture stress because it is a dry day. So, what happens when we get a intense shower the population of the leaf miner decreases and because of the shower the moisture stress experienced by the plant also decreases. So, the plant recovers from the moisture stress. So, such a wet spell is called a drenching shower. Now, again we have to define what we mean by drenching shower. So, we take the rainfall of more than 2 centimeters on a single day within the first 14 days of the leaf miner attack to be a drenching shower. This again is based on the experience of the farmers what should we call a drenching shower. So, leaf miner population will start growing when there are leaf miner days. If in the early stages that is to say within first 14 leaf miner days there is a drenching shower then the leaf miner population will decrease rapidly and we can say that probably they would not be much of a loss. In a season if between 35 and 110 days after sowing see 35 days is when the flowering occurs. So, if between 35 and 110 days after sowing there are 21 leaf miner days and they do not have to be consecutive. Then a leaf miner attack is assumed to have been triggered the loss in yield can be up to 40 percent. So, how do we calculate the loss? We say leaf miner days after sowing 35 that is when the thing begins to flower and the plant has grown and there are plenty of leaves around 35 days. From then up to harvest which is 110 days after sowing if whenever the soil moisture is less than 50 percent of assay and non rainy for 21 days. This is the condition under which we expect the leaf miner attack and the loss can be 10 to 40 percent. Now there will be an attack provided there is no drenching shower. So, if within the first 14 leaf miner days there is a drenching shower that is rain greater than 2 centimeter a day the loss is taken as 0. Then days and losses. So, if there are 25 days of leaf miner then we take the loss to be 10 percent 45 days 15 percent 60 days which is a 2 month long dry spell is 25 percent and of course, 75 days is 40 percent, but 75 days means the entire time almost after flowering has been dry. So, then the plant also is not going to survive. So, this is how we calculate the loss due to leaf miner depending on how many leaf miner days have occurred in the specific season. Now there is another important disease which is called late leaf spot or tikka late leaf spot or tikka is a major disease of ground earth causing considerable yield loss. Now, while leaf miner pest population increases when there are dry spells this tikka infest ground earth when there are wet spells. So, tikka is triggered by intense wet spells during the period 75 to 110 days after sowing. I should mention that there are 2 other diseases which are also triggered by wet spells during the same period and these are color rot and root rot. So, what we will do is we will take wet spells between 75 and 110 days to trigger all of them tikka as well as root rot color rot and then calculate the loss. Now, how do we calculate the loss for each set of 3 consecutive days with very wet soil that is soil moisture greater than 0.9 of the maximum available which is 90 percent of the maximum available the loss is taken as 5 percent. So, each set of 3 consecutive days which are very wet the loss is taken as 5 percent but with an upper limit of 20 percent. So, that if there are more than 4 of these sets then we still take the loss to be 20 percent even for 5 sets like this. If in addition to this there are 10 more days of wet soil and additional loss of 5 percent is observed and this is in fact what is incorporated in the model. Now it is important again to validate this model because we have based the criteria on the knowledge of the farmers. So, we went ahead and validated there were observations at the Anandpur research station of the incidents of leaf miner and tikka and we found that in general they agreed with the model. So, whenever model predicted incidents of leaf miner or infestation by tikka it was also observed in the agricultural research station. So, that gives us a little bit of confidence that we have translated correctly the farmers understanding of the triggering of pests and diseases into the criteria we have put in the model in terms of the soil moisture and what is a wet spell what is a and what is a drenching shower so on and so forth. So, we seem to be on a reasonable right track. See there is another factor that also causes loss of yield to the farmer and this factor is weeds. So, generally farmers remove weeds once around 35 days after sowing. So, weed grow during 35 to 80 days after sowing can have a very large impact on the yield. So, if the soil is very wet that is to say again the same criteria we had used for tikka that soil moisture is greater than 0.9 times the available soil for 7 consecutive days or rather wet which is to say greater than 80 percent of those available maximum available soil moisture for 14 days a loss of 10 percent of yield due to the weeds is assumed. So, there are two conditions either it becomes very wet for 7 consecutive days or it is rather wet for 14 days which are not necessarily consecutive then we assume 10 percent loss of yield due to weeds. So, what is the final thing we take into account in this model leaf miner and leaf miner actually the adverse events which trigger the leaf miner is soil moisture less than 50 percent of the maximum available and non rainy for 21 days and the leaf miner loss is taken as 10 to 40 percent and we have to remember that this loss occurs only if within the first 14 leaf miner days a drenching shower which we define as greater than 2 centimeter rainfall in a single day does not occur. If a drenching shower occurs within the first 14 leaf miner days then the loss is taken as 0 because it is assumed that the leaf miner population has come down and the plant has become revitalized with this rain. Otherwise the loss is 10 to 40 percent depending on how many leaf miner days there are for 25 leaf miner days it is 10 percent for 45 days 15 percent and so on. So, we have assumed what is the loss going to be depending on the number of dry days for leaf miner. For weed growth we have assumed that if soil moisture is great if the soil is very wet for 7 days or rather wet for 14 days then we get a loss of 10 percent due to weed growth. Then we have late leaf spot or tikka which occurs often which is triggered along with collar rot and root rot because the same wet spell triggers this. So, again we take it in terms of soil moisture that if the soil is very wet for 3 consecutive days or it is rather wet for 10 days then for each set of very wet days we take the loss to be 5 percent up to a maximum of 20 percent and we add 5 percent additional loss if there are 10 or more wet days in addition to these sets of 3 consecutive days. So, this is how the losses are calculated now. So, ground at generally flowers in 2 well defined flushes between 70 to 30 to 75 days after sowing. So, so far we have said that wet spells or dry spells within a certain period after sowing will trigger such and such pest or such and such diseases, but there are some diseases that can cause a loss in yield which occur only in certain phenomenological phenological stages. So, for example, pod rot occurs only in the pod formation and pod filling stage and the loss in terms of the fraction of flower loss. So, here now we have to do 2 things we have to determine the phenological stage when will this pod formation pod filling occur. And if there was only one single instance of flowering which we have taken as 35 days that is the first flowering then no problem we can actually knowing the stages of TMV 2 we can calculate which days pod formation occurs and when does pod filling occur. Problem arises because you have 2 flushes of flowering 1 in the early part 35 days or so and 1 in the latter part. So, if we have to calculate the loss due to things like pod rot and so on we have to do more complicated things we have to take these 2 flushes of flowers into account and also then use farmers knowledge to see what the loss will be. And this is much more complicated and I am actually not going to go into details of this, but except to say that there is one more disease I did not mention which is seed rot. So, if we have wet spell for even 2 days within the first 9 days after showing seed rot can occur. And this can lead to a loss of 5 to 10 percent depending on how wet it was and how long it was wet and so on and so forth. Now let us come back to the pod rot problem. So, what happens is that we have flower initiation somewhere between 25 and 35 days and whether it occurs the conditions are given then we have the first batch of flowering. And there is a relationship between the first batch of flowering and second batch because after all the plant is the same plant. So, there are many conditions to be looked into and at the end of it what we find is that the total number of flowers in the first if the first one was good then it would be 100 percent if the second one was good it would be 85 percent and so on. So, there has to be a calculation done of the flower fraction that remains after the 2 batches of flowering. And this during pod formation and pod filling which for the first batch would occur between 50 and 80 days and second batch between 75 and 105 days we have conditions of wet soil which give rise to pod rot. And actually as I mentioned before the losses are in terms of what fraction of the flowering is destroyed by the pod rot. So, this all has to be taken into account and in the full fledged heuristic model that we had developed all this was indeed taken into account the loss of flowers and so on and so forth in calculating the final yield. So, now we have the apparatus ready the model ready to estimate firstly what sort of pests and diseases will attack whether leaf miner will attack whether tikka will attack and so on and so forth. And if so what the loss would be now question is loss from what we already know that the peanut grow model is a pretty good model for the direct impact of rainfall variability it captures the year to year variation in yields induced by rainfall that is to say a peanut grow model actually is a good model for growth and development of the plant in the face of rainfall variability. Yes we know now what we want to do is add one more factor triggering of pests and diseases by rainfall variability and that to do that we have developed this heuristic model. So, how do we now apply the heuristic model to get what would be the expected yield when pest diseases or weeds do attack in the crop. So, what we do is that in fact we assume that the peanut grow model will be will give 100 percent of the yield in other words the yield obtained by peanut grow we take as 100 percent and from that deduct the losses as computed by the heuristic model. Let me just elaborate on this first of all let us see how does peanut grow look versus district yield we have already seen this is the time series we have already seen that when the peanut grow yields are very very high they are much higher than the district yields obtained. So, a nicer way to look at it is peanut grow yield versus district yield and what you find the bias that I mentioned that in general peanut grow tends to yields tend to be higher than district yield is very clear on this scatter plot of peanut grow yield versus observed yield where you know if it was a perfect thing it would have been a on this straight line. In fact there are some points at which peanut grow is less than observed yield, but by far the larger number of points correspond to peanut grow more than the district yield. So, you can see the bias of peanut grow in over estimating the district degree this is very nicely brought out in this slide. Now, in the following slide you will see what happened when we applied the heuristic model. So, here is the peanut grow model here is what we get from the heuristic model and here is the observed district yield and you find that by and large in fact for example, here we have got it on the dot this is peanut grow which was over estimating and with the losses that we calculated from the heuristic model what we get is very very close to the district yield here. So, what has happened now we have corrected for the yields in peanut grow by applying a heuristic model and estimating losses due to pest disease and weeds which were not incorporated in the peanut grow model and have it appears got a better fit with the observed district yield and that is what you see here unlike the earlier one where there was a clear bias with more points above the line which you saw here see here there are far more points above the line in this case in fact that does not happen and the line is sort of in between in the middle of the cloud of points of course, they will not be exact match between either of the models with even with the corrected model with this because there are many other factors that come into play in determining the ground at yield. But overall we seem to have removed the bias that was there in the crop model because it did not take pest and diseases into account. Now you may ask the question so what what is the use of doing this model. So, let me talk a little bit on the application of such models such models for the impact of pest and diseases and weeds are useful in two kinds of decision support systems. Now eventually we are trying to make do a study all this so that we can help the farmers to make a decision which will be optimum so that he will get maximum yield or minimum risk of crop failure. So, how will these models help they can help in management operations after a specific variety is shown. They may help in the decision whether to spray or not spray a pesticide important factor in this decision is the additional cost and expected benefit in terms of enhanced yield. On the basis of probabilities of the attack of specific pests and diseases derived from such models the cost benefit of each of the strategies could be estimated. For example, we find that the probability of a dry spell which promoted leaf miner is 93 percent. This is on the basis of 88 years of data at Anandpur and we find that chance of getting leaf miner attack is 93 percent. But in about one third of these cases 30 percent of such years there was also a drenching shower once a drenching shower occurs there is no loss. So, hence once leaf miner has started growing the probability that a pesticide would be useful is 65 percent. So, on 65 percent of the occasions a pesticide would be useful because you are going to get leaf miner growing in the crop. So, this information could be used in deciding the optimum strategy and I will talk a bit more about the optimum strategy in the next lecture in the latter part of the same lecture. Now, choice of sowing date and variety see earlier thinking that we are given the variety and it is already shown and we can see whether the model will give useful inputs to decision making after that. But the question is how do we choose the sowing date and how do we choose the variety given the rainfall variability of a region. For that tailoring to the rainfall variability of the region to minimize occurrence of diseases such as pod rot for which there is no remedy or diseases which require intensive spraying this model can be useful. Now, why do you want to avoid intensive spraying because increasingly there has been a realization that one should not consume too much of pesticides. So, spraying pesticides on crops is a harmful thing and there is a growing market now for what are called organic crops or crops which are grown without spraying pesticides. So, given this kind of a demand you may want to adjust your sowing date so that in the critical stages for attack of crops you do not get adverse weather events. See this is another way by which one could do it and as I said easy option for tailoring is choosing the sowing window and when we use the same model that I talked about heuristic model and checked what is the probability of occurrence of leaf miner and of tikka given a sowing date. This is the probability of leaf miner and you find that up to 20th July or so the probability of attack of leaf miner is very very high this is because there are a lot of dry days in July, August in this region then this probability dips and it is rather low in this period here from about last week of July till about first week of August. So, this is when the probability of leaf miner is low tikka also the probability of attack is very high for early sowing up to 20th July and then it decreases steadily. So, this is very interesting because what is it saying you remember that when we talked of what is the optimum sowing window for this region we found that actually within the sowing window that the farmers have which is from 22nd June to about 17th August or so we found that the latter part of the sowing window which is from 20th July or so till mid August is more favorable for maximizing yields. Now, it turns out that it is the same part which is also more favorable if we want to avoid leaf miner you see first part of that sowing window that the farmers use the probability of leaf miner is very high and probability of tikka is also very high. So, if we want to minimize losses due to tikka and leaf miner also then it is very interesting that the same window is what is being recommended namely the latter part of the existing sowing window. So, this gives you an example of what we could do to get closer to reality in terms of district yields and how we could use this model to then help in making decisions. Now, so far I have only talked of how knowledge of rainfall variability can be used in decision making how choice of sowing window you know how the optimum sowing window can be determined given the rainfall variability of the region and so on and so forth. Now, remember all these prescriptions that depend on rainfall variability are the same year to year because rainfall variability is a summary statistics of how rainfall has behaved over the region over so many years. But now we have all heard of meteorological predictions that there are actually predictions of how the rainfall will be in the next few days or in the next week or within the next two weeks slowly meteorologists are improving the skill at which we can forecast these events even for larger time scale than 2-3 days 2-3 days already the forecast are pretty good. Now, slowly they are beginning to make a headway into predicting things like wet spells and dry spells at much earlier that is to say few days in advance 10 days in advance or so. So, hopefully those predictions will improve now will it be possible to use these meteorological predictions also for decision support system and as I said here I have been discussing dry spells and wet spells and we have considered probabilities of occurrence of these events for our study area and information about these climatological probabilities is an important input into the decision support system and the question is if we can predict these events can that actually improve the decision making. So, the first response would be of course any additional input would be useful is not it this is what one would think a priori because the more the meteor the more input you get the more you know about the system the better of you will be in managing it this is what would be once gut feeling. But this response does not take into consideration the fact that forecast are never 100 percent reliable. So, given that there is a certain probability of the forecast being accurate one can derive for which decisions it would be useful and this is very interesting and this is a in fact one of the first problems we addressed as a group this is forecasting rain for ground nut farmers how good is good enough how reliable with how much skill does the forecast have to be generated for it to be useful. Now, this is a very interesting concept. So, I thought I will discuss that here. So, what are we doing we are talking of management of pests and diseases of rain for ground nut which we have discussed and plant protection measures and their costs are shown in the next slide. So, we have crown rot in seedling stage which is what we called seed rot and there is a cost of plant protection measure this is a pesticide that you can use and the cost is given here and the typical loss is also given it is only 8 to 10 percent. Similarly, we have talked of ticker disease and what would what would you have to do to curtail it. So, this is the pesticide you have to use and the typical loss is 30 to 45 percent which is again translated in terms of rupees here. Similarly, leaf miner what would you need to control leaf miner 2 sprays of this one and this is the kind of intensity we need and this is the cost you will get cost of spray and leaf miner can lead to a huge loss of 25 to 92 percent. So, estimate of cost of protection are based on the prices of chemicals in 1999 of course, they would have all gone up and typical yield is assumed to be 1000. So, the question is to spray or not to spray that is the question before the farmer and he already has information on the climatological probability of dryer wet spells which lead to the pest or disease and let us now for to be concrete consider only a pest here. Now, so that is why we are thinking of spray or not to spray a pesticide. So, remedial remedial measure is cost C if not applied and if the adverse event example a wet spell occurs the loss in productivity is L which is what we had seen in the earlier table. Now, let the probability of the wet spell be P subscript W P W is the climatological probability we know what the wet spell is we can derive from the rainfall data what is the climatological probability of the wet spell occurring in the critical stage let that be P W. Now, we take the optimum strategy to be one which maximizes the long term advance average returns to the farmer by maximizing the effective maximizing the long term average return to the farmer by minimizing the effective cost that is cost of remedial measure or expected loss as the case may be and I will explain what I mean. So, let us decide look at first strategy is based only on information about climate variability which is what we had looked at. So, consider first the implication of information of P W climatological variability of a wet spell during a critical period. If the farmer decides to spray then the cost incurred by him additional cost over and above his other cost is C and if he decides to not to spray the expected loss is L into this P W because P W is the probability of the adverse event occurring. So, expected loss will be the product of the loss that would have occurred if the adverse event occurred times the probability of the wet spell occurring. So, it is L into P W thus the optimal strategy in this case has to be we want to minimize this effective cost which is C or L star this. So, if the if C is less than this if the cost is less than the expected loss right then we should spray because if the cost is less than the expected loss then clearly spraying is useful. So, we have if the probability of wet spell is greater than cost by loss then the farmer should spray and the farmer does not spray if the probability is less than cost by loss. So, this is how it works out that we are trying to minimize C we want to have minimum of C comma L star P W. So, if C is less than L star P W we want to ensure that this is minimum right and therefore, we want to have probability of wet spell greater than C over L if probability of wet spell is less than C over L then one does not spray. Now, now look at skill of forecast now skill of forecast can be actually assessed by using three statistics P I which is the probability of a wet spell occurring when a wet spell is forecast this means correct forecast of the wet spell. But there are also probabilities of wrong forecast which is to say probability of wet spell occurring when no wet spell was forecast this wrong forecast is P O and P F is simply the frequency with which a wet spell is forecast. Now, the three are related because probability of a wet spell occurring is simply the frequency with which a wet spell is forecast times how often it was correct which was P I plus 1 minus P F is the frequency with which it was not forecast times the forecast turning out to be wrong right. So, if it was not forecast and the forecast was wrong this is the number that you get if it was forecast and the forecast was right then this is the number. So, totally the climatological probability P W is given by this. Now, for models generating an unbiased forecast we expect a wet spell to be forecast on an average as often as it occurs that is to say P F the frequency of wet spell forecast should be the same as climatological forecast. Now secondly for any worthwhile forecast we expect the probability of a wet spell occurring when it is forecast that is correct forecast for occurrence to be greater than the probability of wet spell occurring when the forecast is for no wet spell. At least the correct forecast of probability of correct forecast of wet spell should be more than probability of correct wrong forecast of wet spell this is for any worthwhile forecast. So, we have P i greater than P o. Now, we can combine those two and get P i greater than P w greater than P o that is to say the probability of correct forecast of wet spell is greater than the climatological probability of wet spell which is greater than probability of wrong forecast of wet spell. For worthwhile forecast must be better than climatology this is common knowledge to metrology see unless you can do better than climatology there is no point in generating forecast. Now, constraints on how large this correct forecast probability has to be and how small the wrong forecast probability has to be depends now on the climatological probability. So, without dwelling on it if we are in the this part first week of October then you know P w which is the climatological probability is high it is 0.55 which means that P i must be greater than 0.55 your correct forecast probability of correct forecast has to be rather high more than 0.55, but the constraint is not so much on the wrong forecast because probability of wrong forecast has to be less than 0.55 which is not a very strong constraint. For the second and for on the other hand if we go back to the first and second weeks here of September then the number is more like 0.2 and so we get the condition on P i is less stringent because P i being greater than 0.2 correct forecast probability should be greater than 0.2, but wrong forecast probability should be less than 0.2. So, this is more stringent here. So, it all depends on the climatological probability. Now, consider first the case of a forecast for a no wet spell then the wet spell occurs with the probability of P 0 because this is the probability of the wrong forecast and if the pesticide is not sprayed see the forecast is for no wet spell. So, the farmer decides not to spray the pesticide. So, if the pesticide is not sprayed the loss is P naught into L because P naught is the probability of the wet spell occurring despite the forecast. So, the loss is expected loss is P naught into L if the pesticide is sprayed the expenditure is C right. Hence returns will be maximized by choosing a strategy which minimizes the effective cost which is the minimum of P 0 into L and C right. Now, if L is greater than C if P 0 L is greater than C then spraying is better because this is large and therefore, if P 0 L is less than C then not spraying is better because you want to minimize this the 2. So, you have to make sure that the higher one is not spent on. So, if P 0 L is greater than C then spraying will minimize and if P 0 L is less than C not spraying will maximize the returns. So, what is the strategy if P 0 L is less than C do not spray or if P 0 L is greater than C or that is to say if P 0 is greater than C over L then you spray that is to say remember now the forecast is for no wet spell right. But if P 0 is greater than C over L that is to say probability of wrong forecast is greater than cost versus loss then the recommendation is to spray that is to say the probability of wrong forecast is so large compared to C over L even though the forecast is for no wet spell the appropriate strategy is to apply the pesticide. So, it is saying that everything depends on the ratio C over L when a wet spell is forecast analogously we get expected losses P i L and the cost of spraying C and hence exactly like the before the returns can be maximized by strategy which implies minimum of P i L and C. So, it says not if this P i L is less than C you should not spray if P i L is greater than C you should spray that is to say you should spray remember the forecast is now for a wet spell. So, if we were to go according to the forecast you should spray but you should spray only if the probability of forecast being right is C greater than C over L. So, if the probability of correct forecast is small or of the long forecast is large the strategy recommended is opposite to the forecast. So, here if the correct forecast is less than C over L strategy recommended is not to spray even though wet spell is forecast and I will not get into too many details now except to say that since probability of correct forecast is greater than the climatological probability which is greater than the probability of wrong forecast when you have that the probability of correct forecast is less than C over L then if probability of this itself is less than C over L then P w is less than C over L. This means you remember our discussion on climatological info that the probability of wet spell is small. So, you should the probability of wet spell is less than C over L. So, hence the recommended strategy of not to spray is the same you would say probability of wet spell is small. So, do not spray and that is exactly what you get by recommendation same thing we can see if what happens when wrong forecast probability is greater than C over L that also implies that what you are doing then is going against what the forecast says but exactly what the climatological probability would tell you to do. So, when we get a strategy depending on climatological probability we can add to that in terms of decision making only if probability of the correct forecast is greater than C over L and probability of the wrong forecast is less than C over L. So, use of forecast will yield a different strategy from what you would have got from climatological information only if probability of wrong forecast is less than C over L which is less than probability of the right forecast. So, the lesson take home lesson is that how good the forecast has to be for it to be useful depends on the C over L ratio C is the additional cost incurred and L is the expected loss due to the attack of the pest. So, it depends on what application you have in mind for decision making you cannot have a blanket statement saying the forecast is good or bad you have to for it to be useful in a specific application you have to see whether the probability of correct forecast is actually larger than C over L and probability of wrong forecast of the same event that is to say event occurring when it was not forecast is less than C over L. So, it all depends on what applications you have in mind you will be surprised to know how many meteorologists are in fact ignorant of this basic fact and talk of skill of forecast being good for the farmers or good for application without reference to the specific application you had in mind or the specific decision that the farmer was going to make based on the forecast. So, this is an important take home lesson and what we have learnt in this set of lectures is that there is a lot to be learnt from analysis of the climate variability of the region a lot can be achieved by tailoring either the crops varieties or management practices such as showing that to the rainfall variability of the region about that there is no doubt that one could get better yields by doing this one can also get less losses by pests and diseases by tailoring to climate variability over and above that if we have very good forecast that is icing on the cake and those forecasts however have to be good for the application in mind the probability of correct forecast of that adverse event has to be greater than C over L which is the critical ratio that comes out of here critical parameter which has to be greater than the probability of wrong forecast that is to say event occurring when it was not forecast only then forecast will add value and decision making of the farmer will gain because of the forecast and yields over in fed regions which are so sensitive to climate variability will actually improve. Thank you.