 Next topic, I would like to introduce about conjunctive use and how to apply our conventional linear programming for this conjunctive use and how to apply the fuzzy logic or fuzzy linear programming in conjunctive use. I have just given an introduction, normally if you see up to 1970s or 80s, 90s, separate models have been developed, large number of optimization techniques to match the supply and demand using many you can say soft computing techniques for surface reservoir operation separately and ground water operation separately, right. But the combined strategy which is the actual practice in the real life was not done much, people have tried, but they have failed and not much literature has appeared on this conjunctive use, everything has stopped only up to the dynamic programming or stochastic dynamic programming, after that we could not go much on this conjunctive use because of large number of variables involved, even surface water reservoir itself is a complex problem and ground water optimization techniques are all much complicated. If I want to mingle these two, then that is almost very difficult to do and optimization. So in such places we try to do certain assumptions, we do from distributed modeling, we go in for lumped models, that means we average certain variables and try to manage the situation and that is why management of surface water and ground water separately, extensive work is done by considering deterministic values, right. We average it over a period of space and time, whereas when I consider the stochasticity in the model, most of the works for surface water we might have heard about stochastic dynamic programming, we consider the stochasticity in the inflow or stochasticity in the reservoir rainfall, these two are the stochasticity considered, whereas nobody has done considering the stochasticity of ground water level variations. It is also a stochastic variable, I like to give an introduction about conjunctive use. Conjunctive use is defined as the planned coordinated combined utilization of surface water and a ground water, right. So I have three objectives here, the first objective is to develop optimal operation strategies for conjunctive use of surface water and ground water and then to study the feasibility and adaptability of fuzzy programming technique in deriving optimal operational strategies for a reservoir aquifer system. And then the next one is to develop a stochastic dynamic programming model considering the stochasticity of both surface water and ground water. And then to demonstrate the use of developed fuzzy and stochastic models in two different irrigation systems, because in real life we will never encounter a system which has stochasticity in both inflow as well as ground water level variations or we never have a situation where we need conjunctive use. So this is different types of conjunctive use we come across in the world. You know conjunctive means using surface water and ground water. I have a command area which has the total command area, the surface water and ground water are mixed together for a given season. That is also a first type of conjunctive use. In some places the entire command area, the surface water is used for some time period and ground water is used for some time period, this is the same command area. We call that as second type of conjunctive use, third type of conjunctive use is the same season part of the command will receive surface water and part of the command will receive ground water. So it is only a combination of spatial variation, temporal variation of utilization of surface water and ground water. Then the last type of conjunctive use is mixing of good quality of surface water and poor quality of ground water or vice versa and using it for irrigation. That is also categorized as conjunctive use. So this is the chronological development of conjunctive use. Conjunctive use is invented accidentally after two major droughts throughout the world in 1940s. So mathematical description of conjunctive use first was given in 1965, after that it took a different deviation, they thought that it is only a stream aquifer interaction problem rather than an optimization problem. So it is only in 1975 or 1980s it was considered as a system analytical problem and it was greatly divided into three techniques, one is optimization mainly to derive the optimal cropping pattern. We have seen literature on linear programming, dynamic programming and non-linear programming. And for optimal allocation, they used both optimization and simulation. Whereas this optimization and simulation technique, this is where many people are working. They use these analytical models and simulation, analytical model to determine the head of water available in the aquifer and simulation to determine the release from the reservoir. So these are all some of the limitations which we go in for real life based upon which we have classified our objectives. Suppose if I do, we have done PhDs and all these things, what we will do is to determine the demand. We use the most sophisticated model, either it is Penman model or Penman-Montyeth model, Blanik-Riddle method, whatever it is and then derive our optimal operating reservoir policies and try to compare it with the real life, it will never match. The main reason is the estimation of this demand. In real life, the releases are based upon not your Blanik-Riddle method or Penman-Montyeth method, that is based upon the conventional duty delta method. So that is why whatever the fine-tuning soft computing techniques we apply in reservoir operation, it will never match with the real life, because we differed from the starting stage itself that means estimation of demand is not the same as what we estimate using soft computing techniques. So what is that difference, if you are able to find out that difference and your model and actually is only that difference that means we can say that estimated using soft computing techniques is more or less fine. So we have done a small work to determine what could be the difference between actual real life method what people are using in the field based upon duty delta method and what is the difference if I use a more sophisticated soft computing method like Penman-Montyeth method or Penman method. Then second one is we used our optimization and simulation for our conjunct use. Then next is we used fuzzy optimization technique for the same problem to prove that, because fuzzy optimization technique is very easy to develop rather than any complicated stochastic dynamic programming. And then finally we developed a stochastic dynamic programming model and compare the results. So this is the first methodology estimation of irrigation water requirements and its comparison. Then second phase is optimal cropping pattern using fuzzy linear programming and a linear programming model. We took two case studies, one is water deficit environment, another one is water logging environment because conjunct use is not only required in water deficit environment, it requires in water logging environment also. There is a different classification for water logging, physically people think that water logging means appearance of water on the ground water. That is not the criteria for water logging classification in an irrigation system. If the water table is within the root zone, we classify that area also as water logged area. And different state governments they have their own methodologies to classify the areas under water logged condition. So in the present study area we took Sriramsagar project as the case study. And the third methodology is application of stochastic dynamic programming. Here we consider the stochasticity in surface water inflow and stochasticity in the ground water variables. So we have selected two case studies, one is lawyer Bhavani reservoir project which is a water deficit environment in Tamil Nadu and Sriramsagar reservoir project which is under water logging environment in Andhra Pradesh. So this is about lawyer Bhavani reservoir project, it is a tributary of Kaveri constructed across river Bhavani which has a capacity of very small 928 million meter cubes. The total command area is 1 lakh, why we have classified this as water deficit environment is it is not the availability of water, yes every year this reservoir gets filled up. But still we classified this as water deficit environment. Because the main canal is 201 kilometer, why I am telling is this before solving any water resource problem I said first one is we have to understand our water resources system. It is not simply applying the technique and getting the solution. So here even though the total command area is 1 lakh hectares, every year we could not irrigate all the 1 lakh hectares. But the dam is designed to irrigate this 1 lakh hectares of dry crop. But during the initial phase of operation and the reservoir was open the farmers have shifted from dry crop to wet crop. So first 5 years it was very good, first time water was coming from the dam, all the people it took 5 years for the farmers to shift from dry crop to wet crop. So after construction of the dam within the 5 years all the 1 lakh hectares are under paddy crop. So even though you have water you cannot release it. Because the canal carrying capacity is fixed based upon the dry crop method. So what happened the government could not release the total area and there was a huge cry among the farmers. Even though there is water in the dam it cannot be opened. So what happened there was a huge clash between the people and 30 years back there was a big fight more than 400 and 500 farmers have been died in the clash between the police and the farmers. So there was a water users association formation and there was a setup to discuss about this problem how to go about technically. So which will be compromised by both the people. So what happened they agreed they don't want to come back to the dry crop. They want only wet crop. Technically for us it is not possible to release the water required for wet crop. So we went for a different type of methodology that is called turn system. That means the total command area will be divided into 2 parts alternative command areas alternative sluices that means only 50% of the area will get water this year. And remaining 50% of the area will get water only next year. That means even though the potential created is 100,000 hectares every year physically only 50,000 hectares gets water. So that is why we classified this as water deficit system and gradually what happened suppose if this system was very badly classified the alternative sluices are considered for irrigation. So what happened when next fellow is getting water this fellow will not keep quite. So he started pumping the groundwater. So because of this the seepage losses have increased and even that 50% area could not be irrigated. So that is the status of the physical system before going into for our modeling. That means conjunctive use is inevitable there. So this is a lawyer Bhavani Reservoir project. Unfortunately it comes under Kaveri basin, it is a tributary to Kaveri. So one of the huge reservoir it holds the Lemka book of records that the longest earthen dam is in this lawyer Bhavani Reservoir. Around 8 kilometers is the length of the earthen bund that much quantity of water is there. It has this is the main canal which was constructed and created the problem. Then there is another physical constraint in this is before creation of this problem these are all the three canals called Arinaayagipuram canal, Thadapalli and Kalingrayam. They are having the riparian rights. So that also should be encountered in the models. Because whether you release water for your new canal or not I have to release water for my old command area that is the riparian rights. So these are all the detailed canal system and operating dates after discussion with the Farmers Association. So the Kudiveri Annicket for Thadapalli this is the command area and the opening date and closing date is full year. So throughout the year that fellows will receive the water. Whereas Arkankottay also same time period it starts from April and it ends February of next year. One month is the time period. These three are under riparian rights and this is the area where we have to model. So out of 1 lakh hectares approximately 41,000 only will receive water in one area and 45,000 will remain in the next year. So how we divided the systems turn system. So it is based upon the year odd calendar years and even calendar years. The sluices are numbered the 1, 2, 250 there will be 1, 2, 3, 4. So this year only odd sluices will receive water even sluices are shut down. So you cannot receive surface water. In the next year the odd sluices are closed and even sluices are opened. Only two crops water will be released because my canal carrying capacity is fixed. But even though we try to do only surface water modeling in reality there is conjunctive use also. So we estimated the groundwater availability suggested by Groundwater Estimation Committee norms in 1997 I think many people might have used this one. This uses the groundwater level variations observed in the observation wells specific yield and the area of influence of each wells. The another technical problem we encounter when we use this GEC norms is what is the area of influence of each observation wells. There are 27 to 50 observation wells in this 21, 201 kilometer square. So we just adopted the methodology of using the same technique which we have adopted for rain gauge stations. We know that this is not the correct method. Because the main assumption in using this in polygon method is the variation of the variable from one station to other station is linear. But it is not linear in case of groundwater but in the absence of any other data we don't know what is the groundwater level variation from one observation well to another observation well. Even after drawing the fence diagram we are unable to get down what is the water level variation. So we have just adopted this one and we got approval from the Chief Engineer of Gump of Tamil Nadu for this one. So this is how the water level varies over a period of time. This is done in 1997. So the starting month is from 1971 to 97. So within 27 years this is water level variation within each month. The trend has increased that means the depth of water level has goes on decreasing because of over-exploitations. So once we have applied our groundwater estimation committee norms and estimated the groundwater availability for each and every month. So we found that the groundwater is available when there is no release from the reservoir. That means it takes some time period for the water to reach the groundwater. We have estimated this one. And another assumption in groundwater estimation committee norms is the groundwater pumpage is equal to groundwater recharge. The next case study we have selected is Sriramsagar project. This is on the other hand. That means most of the area is under water logged condition. We can just compare the capacity here the capacity of Sriramsagar project is 3172 million meter cube and dead storage is 850 million meter cube. In my water deficit environment the total capacity is only 927 which is equal to the dead storage capacity of this reservoir. So this Sriramsagar project it has 3 main canals. So as a mathematical modeler we drive this type of diagrams that is called schematic representation which gives all the technical details. I think this we know everything. Only thing is this is the main canal, Kakatiya canal which is 369 kilometer square is the command area. Here the problem is water table is within the root zone depth. So groundwater estimation committee gives different methodology to estimate the groundwater available in water logged area and this is the formula. The groundwater at a given time period is equal to 5 minus where 5 is the assumed depth. If the water table is within 5 meter from the ground level groundwater estimation committee has classified that as a water logged area. And WLT is the water level from the ground level, SY is the specific yield and A is the area of influence. And instead of considering 5 meter since in this area the water logging is acute we estimated what is the volume of water available in each 1 meter cake of the aquifer. So this is the criteria for water logged condition by the state groundwater department government of Andhra Pradesh. If the water table depth is shallower than 2 meter below ground level during April month that's very important. That means it's a non irrigation period and that is the peak summer. If the water table is within that time period 2 meters then the area is delineated as water logged area. If the water table depth varies in between 2 to 5 meters below ground level during April month then the area is delineated as prone to water logged area. Why they called as prone to water logged area is within no time this 2 to 5 meters will be within the 0 to 2 meters. So this is the water level variation within 30 years you can see that it is in between 0 to 6 meters. This is a sample well it goes on the water level came very nearer to the ground and in 1980s they have developed a policy it is called conjunctivus policies the farmers are forced to draw groundwater by stopping the release from the reservoir. Then it has picked up and slightly it has increased but it is not increased much still the areas are under water logged condition. There are 680 observation wells in this command area because the problem is very accurate the government doesn't know what to do but at least they observe the physical system to understand may be useful by other people they observed the water level variation before monsoon and after monsoon and the 680 observation wells. If you see this one we have classified that into 3 broad categories water level within 3 meter below ground level that is water logged area water level between 3 to 5 meter that is black color that is prone to water logging area water level more than 5 meter that is free from water logged areas. So the water logged area it has gradually increased and suddenly there is a drop because of conjunctivus operation in 1984 after that also it was maintained but not to the some extent because the farmers has to pay power charges that is the main criteria for the water logging in this area. The other thing is almost this prone to water logging area remains almost constant that means more and more in the other hand even though this water logged has reduced the area which are not water logged are coming under prone to water logging area that is why this second category is always a constant and this is same technology we use to determine the ground water availability this is part of this Kakatiya canal and how to estimate the influence area for each well. So for our model to consider the stochasticity we considered each 1 meter cake of the aquifer and estimated the ground water availability for each 1 meter cake. So if my ground water depth goes on increasing the volume of ground water available also increased the another better thing or we can say that the another good thing in this command area is the water is not saline suppose if this water is saline then I cannot utilize it for conjunctivus fortunately in this command area still the water quality is within the Indian standards so we can go in for a that means quality problem does not comes into the picture is a physical status suppose if the water qualities are not to the Indian standards of irrigation water then as a modeler I have to incorporate the water quality problems also now that variable is avoided so this is about physical system. So as a first system first objective we just compared I think this we might have done very well the estimation of irrigation water by modified penman method and duty delta method then after doing this we found that the difference is large the difference is very large so we improved a or introduce a new methodology that is called improved duty delta method that means duty delta method we never incorporate the effective rainfall we never incorporate the stages and we never incorporate the losses whereas in improved we we could not incorporate the stages in the crop however we have incorporated the effective rainfall and efficiencies so this for just for comparison the quantity is very less but they are all during water stress periods I will tell the conclusions in the last so the results on this comparative study we consider the modified penman method as the standard method the duty delta method which is in the field it has overestimated for irrigated dry crops they release more than the requirement and it has underestimated for wet crops because non-consideration of crop stage effective rainfall and other climatological variations whereas in our improved duty delta method the results are very nearer to modified penman method which is very easy to estimate and can be implemented in the field first is on water deficit environment is the case study two different programs the advantage of linear programming and fuzzy linear programming is we have to slightly modify the linear programming to convert it into fuzzy linear programming we don't need to do a great modeling changes so this is the methodology we have adopted we developed a linear programming model subject to maximization of net benefits and subjected to physical and economic constraint we have done for various scenarios that is without conjuncti use with conjuncti use with 70% and 90% dependable inflow levels then I if I consider this as the conventional soft computing technique this fuzzy linear programming is the modern soft computing technique for the same problem we developed a fuzzy linear programming model we never fix what is the input whether it is deterministic or we give only the range minimum maximum low high or whatever the ranges so we consider the I think I will go through this very fast this is the objective function maximization of net benefit subjected to water allocation constraint with the efficiencies of surface water and ground water this is the downstream side release because in lower Bhavani since it is in Kaveri sub-basin a definite quantity of water has to be released in for each and every time period that is the minimum it can go for a maximum so this is a site specific constraint other constraints you can see in many models then next important is the ground water extraction at any time period should be less than the permitted quantity that is equal to the estimated quantity and all my surface water releases should be less than the canal capacity so this is area constraint algebraic sum of all the area should be less than my total area continuity constraint or the system can mass balance constraint and the last one we are able to incorporate is called overflow constraint because overflow is a nonlinear term that means over flow occurs if my storage is more than the capacity so there I have to take a decision as a nonlinear term which it's not possible in linear programming only nonlinear model can take care of this one so we linearized that nonlinear equation using these two equations so this is the evaporation relationship based upon the observed values we developed a linear relationship between storage and evaporation all right I think fuzzy programming yesterday I gave some example for deterministic I am not remembering that that variables right so it is within the ranges so fuzzy programming is the real life solving problems I think the first place where fuzzy programming was used is in in a subway operation of the signals how long the signal has to be on that depends upon the number of vehicles on the queue right so in India the first time fuzzy programming was used in our washing machines at videocon fuzzy washing machines that means the time period required for rotating depends upon the weight of the cloth we are putting so each day we cannot weigh correctly and keep it in your machine so they gave the range if the load is between weight of the material is from this value to this value then output is this time period if the weight of the material is between this weight to that bit fixer then your washing machine time is different so as we all know that these deterministic approaches output is also crisp whereas stochastic approaches are very difficult to model we can say that is a conventional technique but is still no computer can solve a real life stochastic dynamic programming if my number of discretization is more than 15 I think even if you have a Sun micro systems it will crash so that is why we invented this soft computing techniques reason techniques right and also other disadvantage of the stochastic approaches it cannot handle statistical uncertainty whereas fuzzy theory which was introduced by Zimmerman can handle the non statistical uncertainty non statistical uncertainty is vagueness imprecisiveness in the data or we call it as in conventional outliers only we remove the outliers in our time series and do the modeling whereas our soft computing techniques can take care of even the outliers we no need to do the data processing so this is a simple classical linear programming model maximization constraint in fuzzy linear programming model we have a different way of giving the input in the form of a membership function that means here my objective is to maximize the satisfaction level in my deterministic linear programming my variables may enter into the solution space or may not enter whereas in real life I have all I should have all the variables in the solution space may be with different satisfaction levels so the satisfaction level for each and every variable varies in between 0 to 1 whereas in linear programming it will be either 0 or 1 so here my satisfaction level varies in between 0 to 1 and I can compromise on certain things first one is instead of having a benefit of Z I can go in for a benefit of Z minimum that means I am able to reduce even my net benefit from the system thereby I can increase my satisfaction level at the same time instead of giving me a constraint of or a resource constraint of bi I can give a little more constraint also or little more resource also there are different ways of expressing this membership function the membership function what I have listed here is one side a triangular membership function we have continuous triangular membership functions we have trapezoidal membership function that depends upon the variables in our hand or the data set we have in our hand this depends upon the modular and depends upon the data set in hand if we are able to classify your inflow into n number of ranges then I can have n number of triangular membership functions but here the data is very small link we have classified only as a simple one-sided triangular membership functions right so in this model my objective is maximization of this value either 0 to 1 if my satisfaction level is nearer to 1 then my goal is achieved so what I do is I compromise to certain extent in this level so that I use the increased resources very little and maximize my net benefit so here my objective is maximizing the satisfaction level and my previous constraint in the linear programming will become objective function will become a constraint so wherever we have the fuzzy variable we introduce this lambda right particularly in in this case we have considered the fuzziness in the objective function in the downstream river release inflow and ground water availability that means we are not crisp in my objective function I assume I can have a lesser objective function values and minimum river release no need to go in for a deterministic value of minimum standard or average standard I can little reduce the downstream release thereby I can release water for irrigation and increase the net benefit and inflow need not be a maximum value it may be less values also so if it is lesser and lesser my satisfaction level goes on reducing then my ground water availability instead of using an average I can pump a little more so with this membership functions the modified linear programming will be like this linear programming the previous goal constraint will become like this and downstream side release will become negative that means whenever I have a membership function of towards zero negative then I have to subtract the satisfaction level when it is away from the zero I have to add my membership function so this is ground water availability is away from the zero I am adding it that means my resources are increased whereas in river release my resources are decreased in objective function my resources are reduced so I am subtracting adding and similarly in inflow is towards the zero value when I take it on the other side it will become negative since it is an unknown value I am taking it on the right side similarly overflow constraints so this regression analysis that is input to my model right and once if I do that one that is a regular linear programming only I am not using the complicated MATLAB programming and all these things simple linear programming converted into a fuzzy linear programming but again that fuzzy linear programming itself is similar to my deterministic linear programming but I have incorporated the fuzziness of all the variables in terms of numbers in terms of ranges suppose if my input is in linguistic form then I cannot use my revised simplex method to solve this I have to use some other technique this is to simplify we made it as a fuzzy optimization it is not fuzzy logic technique it is fuzzy optimization technique if I have all the inflows in terms of linguistic high low medium then I have to solve my fuzzy model using fuzzy logic technique rather than fuzzy optimization technique here I did only fuzzy optimization technique so once if I do this then that will be easy to solve I have used here revised simplex method to solve the simple fuzzy linear programming model and this is the comparison right so the releases with actual and LP model and different scenarios 70 percent dependable inflow 90 percent dependable inflow and its ground water more here is when I use the ground water when I don't use my ground water this is my downstream river release because the main objective here for the government is how much water I can release from this command area to Kaveri so the chief engineer is more concerned about this downstream side release rather than his own command area release so here we are trying to maximize this downstream sewer release and the same time we are maximizing the net benefit so if I use conjuncti use the quantity has increased 300 million meter cube which is one-third of the capacity of the reservoir so this is a trade-off if the dependable inflow goes on increasing normally 75 percent is the average value we use in reservoir operation if the percentage goes on decreasing inflow is more and if it goes on reducing we have to do the sensitive analysis of my optimization model so this is ground water pumpage if x is the available quantity if I pump we can pump more and more water but only thing is your objective function cost will go on decreasing so this is the fuzzy linear programming model it was so astonishing to see that the downstream side release is more than the capacity of the dam so the capacity of the dam is only 827 927 million meter cube when I use fuzzy linear programming model we are able to release thousand million meter cubes so as a modeler we finished this but as a policy makers they have to implement it in the real life they will never implement it right then the next problem is the first question it arises is where does this water comes from in real life the capacity is 927 if you say release thousand where from where I can release so the main thing what fuzzy program did is it has maximized the ground water utilization so that is where the real life the chief engineer does not have any control on ground water utilization that is why even though we are able to give a solution it is not able to be implemented in real life this variable we cannot incorporate it in our model forcing the farmers to use only ground water so the next place where we have used this in water logging condition in swar says on the soccer project same problem I think here the objective function is little bigger because there is a cost involved in using the surface water and ground water this objective function should also be constrained or formulated based upon the site condition in previous case there is no cost for the farmers to pump the ground water current is free only initial cost is involved whereas here the farmers has to pay for surface water as well as for ground water so if they use more and more ground water their net benefit go on reducing because the cost of using ground water is three times the cost of surface water so there are other constraints remains the same the storage capacities the another important in this area is this socioeconomic constraint I call this as socioeconomic constraint because each and every area there are more than 17 crops in this command area however government has classified only 9 or 8 crops mainly I will show you these crops these are all the major crops classified by the government to incorporate in this there will be rice mice ground net sunflower other irrigated crops sugarcane and we have two bi-seasonal crops only these crops we can consider for our modeling purposes so we have to give minimum area for minimum area for each and every crop that is each and every season there should be a minimum area under this crop we classified this as a sociological constraint and this is our evaporation constraint here since we don't have downstream side release my fuzzy linear programming will have only three fuzzy variables that is fuzziness in gold fuzziness in inflows and fuzziness in ground water pumpage and this is the modified FLP model only four or five places we no need to modify all the constraints each constraint is 12 in in previous case in this case each constraint is 36 because there are three canals each canal applies 12 constraints monthly model three canals it is 36 model so totally we had more than 196 constraints and around 154 variables and this is the time series plot or the input into my model is inflow into the reservoir and the statistical characteristics the cropping pattern these are all the input to the models the monthly net irrigation requirements the relationship between evaporation loss and monthly storage then once I give this input I can develop various combination of policies alternative solutions in previous case we have not derived any alternative solution that is not required because my objective is fixed so that is the main criteria of showing this is we can do any type of modeling for a given problem but we have to select an appropriate model based upon the site specific condition that is why even today there is no single algorithm is available to solve water resources problem common so each and every problem you create will apply only for a particular site so here we developed a combined optimization simulation that means we developed the optimal operational plans and then we simulated this condition for a longer length so since there are so many variables are involved we have given priorities rice is the first priority technically possible here large quantity is available all the area will go can go under paddy crop unfortunately more than 35% of the command area is under waterlogged condition even though paddy is a water loving plant it will not grow under a waterlogged condition it need water only on the top not on the bottom so the conjunctive use will help in two ways one is it will eliminate the area under waterlogged condition second one is since the quality is good the same water can be used for irrigation so based upon the priority of rice crop and priority of groundwater pumpage we have developed some 45 scenarios various alternative solutions I will just show only the scenarios the scenarios are like this highest priority to rice crop 75% priority to the highest that means whatever the area comes as the highest priority of rice crop reduce it to only 75% thereby we will reduce the area under rice and increase area under cash crop thereby increasing the net benefit then restrict the area of rice to 50% of the maximum possible so that means other area will be under cash crops then similarly pumping level reduce the target pumping is only one meter because when the depth of pumping goes on increasing my net benefit goes on reducing because of more head on pumping the farmer has to put more powers to pump the water so on the other hand if the depth of pumping goes on increasing more and more area will come under irrigation because more and more area are free from waterlogged conditions so these are all the targets and these are all the tradeoff or tradeoff is relationship between these things that means when my pumping level goes on increasing when the depth of water is below 3 meter only I am able to achieve 200% irrigation intensity so when I implement the policy to use the groundwater within 3 meter I may not able to irrigate 200% irrigation intensity so this is full policy maximum area under rice then also I will not have more area under irrigation so this is the net benefit when depth of water pumping is more than 3 meter or 4 meter the cost of volume because volume of pumping is more my net benefit goes on reducing so this is the tradeoff this is the optimal cropping pattern only 2 to 3 crops will decide your net benefit so these are all the comparison of result optimum results from LP model from FLP model if you see the quantity of water utilized is almost same the only difference is which water we are using here we are restricting the FLP model to use more groundwater than the surface water thereby it increases the area under irrigation and makes the area free from waterlog at the same time it increases the net benefit so then we select the since there are so many policies we cannot use the all the policies we can select certain policies which are developed through a simulation model simulate that policy for longer time periods that is optimization simulation technique and we used this thermosphering model to generate 110 years of inflow data and first 10 years was discarded to take care of the initial condition 100 years of inflow data was used to simulate this condition if I implement this policy for 100 years what is the benefit and we found that the deficit in the system is only 5% I think we I will do it in the conclusions in the this is the result of simulation in the simulation I can see what is the percentage deficit period out of 100 years zone one is for each canal we can do then percentage deficit in demand that is in million meter cube what is the average deficit for 100 years what is the surplus here without conjunctives and with conjunctives the thing is we are improving the surplus thereby increasing the quantity of downstream river release in godavari also where it is mainly needed in the downstream flushing and downstream navigation so these are all the major conclusions from comparative estimation of irrigation requirement we found that duty delta method underestimated the irrigation requirements and it has overestimated for dry crops and the optimal results of LP model shows that conjunctives is inevitable not only in water deficit environment but also in waterlogged environments so these are all the satisfaction levels that means I am able to incorporate all the variables in my solution space there is no zero variables in my solution all the variables are into the solution space but with a satisfaction level of 0.64 in water deficit with 0.718 waterlogged environment so we did a sensitivity analysis also in water deficit environment fuzziness in surface water that means instead of giving all the fuzzy variables at a time we do a sensitive analysis of giving fuzzy variable one by one so if in this we can find out which variable is more fuzzier than other variable and we found that surface water plays a greater role in fuzziness in water deficit whereas in waterlogged environment fuzziness in groundwater played major role in deriving the reservoir operating rules or cropping pattern right so these are all the two policies which we have selected first policy is there is no restriction of the rice crop because this cannot be imposed on the farmers so farmers can grow as much as rice crop but they have to keep their command area groundwater below 3 meters then the second policy is restrict the area to seventy percent of the maximum area but pump the water from 4 meter of the ground levels so these are all the three references which has been published from best upon this work I think this SDP model SDP and GA which we have applied I will take it in the next class what is that so I think ten minutes any questions no more groundwater more groundwater groundwater is the first priority that was that was estimated through our GEC norms in this model we don't have the interaction between stream aquifer this is not stream aquifer interaction model if I want to incorporate the stream aquifer interaction model I should develop another finite difference or finite element model whatever the head causing head you are getting as the output that has to be incorporated in GEC estimation here I have made that ground water availability as a deterministic value will also increase yeah so no that is not considered in this that's what I'm telling in this model it is not considered if you want to consider that here what happens we are estimating this right see this values are estimated from the interaction between your releases and the ground water level variations here I consider this as deterministic value suppose if I want to incorporate that stream aquifer system instead of giving this as the input I have to give the input of your output from your stream aquifer model finite difference or finite element and then reestimate this for each and every time step so if I incorporate more and more variables my complexity increases