 So, yesterday we have completed up to this sequential decision models in water resources. But in water resources, we encounter not only the sequential decision making problems, we encounter the problems where we have to answer what if conditions, right? Because so many probabilities, so many stochasticities are involved, I need to find out what happens if it does not happen. So, that should be clear even before implementing it in the real life. So, that when I went after modeling, if I go there and if I implement and if it does not works at that step, I cannot go back and do the reverse modeling. In hand, I should have a solution. If my solution at the current time period does not works, what is the alternative solution? We call it as what if condition. Unfortunately optimization models will not answer this what if condition within the planning period. The best technique to apply this what if condition is simulation techniques, right? These are all the techniques which can answer what if condition. So, I have given some example of simulation. What is simulation? It is nothing but reproduction of working condition. Good example which I used to give to my students about example, because our students will always catch the examples very easily. If I want to go for a movie, right? Before actually entering into the process of going into the movie in the brain, we used to do a simulation job. That means we start with what movie to be gone, which theater with whom we have to go, what time we have to start from here, what is the mode of transport, if ticket is not available, which theater, which movie we have to pass, with whom we have to go. When we are coming back, if the vehicles are not available, how to come back, if the hostel is closed by that time, what happens for our lunch or dinner? So, alternative solutions each and every prop which and every event, we do two decision. Yes, no, yes, no. So, you have a path, you can pass through various SS, you can pass through various no, no. Finally, the job is done. So, that means without actually entering into the field, we draw a conclusions based upon our what if conditions. That is what we called as simulation. That means we are reproducing virtually the system in the computers or we are virtually reproducing through the soft computing techniques. And we call that as digital reproduction. There are certain physical simulation models also, which is a time consuming job. Very easy to do a soft computing simulation technique rather than a physical simulation models. That is why I said mathematical models are soft computing models. So, these are all definition I think we might have done so many simulation processes. I am not going in detail about this simulation processes. Simulations are more useful to determine the input conditions and also to determine which are all the important components in a designed water resources system. And nowadays we are not doing this system behavior using simulation, we are doing only system analysis using simulation techniques. That means finding out the interrelationship between the variables. I think this we do not need to go each and everything it is well available in many textbooks. I have just classified what are all the types of simulation. Like our optimization, we do not have different types of optimization techniques to get a solution. But whereas simulation based upon the time step, based upon the solution techniques, we have different classification particularly short run simulation. If I simulate my virtually if I simulate my water resources system within the planning period, normally for our water resources system the planning period is one year. If I simulate it within that one year, then I call it as a short run simulation. If I simulate my water resources system over a long period, more than one planning period I call that as a long run simulation. Then we have time sequence simulation similar to our hydrology. Here the time step is fixed. In event sequence I look only for the particular event to happen. Then based upon the input condition, it may be a deterministic simulation. It means if my input values are determined, deterministic. Stochastic simulation is if my input variables are stochastic or probabilistic. Next one is steady state simulation and transient simulation where we encounter mostly in our finite difference modeling or finite element modeling. Steady state solutions and transient solutions. That means steady state solutions are solutions achieved for the given set of input. What is the final output? Transient solution is when the inputs are going on changing. It is a deterministic but the input values are going on changing. So these transient simulation models are very important and very useful in groundwater studies. Your mud flow, you can do steady state simulation and you can do transient simulations. But in real life as in water resources we don't have separate models. It is only combination of any one of the above. Then what are all the steps required for simulation? First one is we have to identify the components, identify the variables. As we all know just for theoretical purpose, there are three important words we use in water resources. One we call it as a variable and one we call it as a parameter and one we call it as interrelationship. So a variable is a physical quantity which varies with respect to time and a parameter is a physical quantity which does not vary with respect to time. For example inflow into the reservoir is a variable, varies within the time at least within the planning period. The carrying capacity of the canal or the capacity of the reservoir it does not vary within the planning period. We call that as a parameter. Then relationship we know. Similarly based upon these variables again we have different categories. We are called state variables. I have listed it, input variables. State variables are the physical parameters which gives you the status of the system for any given time period. For example storage at a time period, evaporation loss at a time period, seepage loss at a time period. Input variables are the variables which we give as the input to the system. Based upon this input only the simulation model will able to give the output. Then output variables are they are the variables which comes as the output based upon the input what we have given and based upon our objective function. Then there are some other two important variables that is called exogenous variable. They are not part of the system but it may be incorporated within the system. For example historical inflow which we give as the inflow is the input variable. For example if I am going to plan my reservoir for 100 years then I may not have a historical inflow. So what happens? We generate a 100 years of inflow and we give that as the input and such inputs are called exogenous variables and we have endogenous variables which is the byproduct of our output. Even though we are looking for only particular releases indirectly we may get what is the monthly evaporation loss, what is the monthly storage, what is the different types of crops. They are called exogenous variables. Target variables are the exact variables which we need and which we use it in our objective function. So these are all the second step identifying the variables. Then identify the relationship between your variables like your optimization model and then fix your time interval in your simulation model. If you have larger time intervals then your simulation will be faster, your accuracy will be very less. When you are doing it for a fine time periods then it takes longer time and your accuracy will be very high and this time interval highly depends upon the objective function. Suppose if my objective is only for reservoir release then I need a seasonal planning or at least entirely planning model. If it is for power production then I need an hourly time step simulation model. Since we have two broad classifications in optimizations and simulation I have compared the differences between optimization and simulation. I think this is the reason I have given this in the notes and this is available in many books also. You can just go through this for want of time I am skipping this. So this I have already explained status of water resources today why we are studying water resources engineering and somebody was asking the title is soft computing techniques. The techniques which I am talking does not belong to soft computing techniques but according to me even though the solution methodologies for these optimization techniques and simulation techniques are well defined. Solution technique for linear programming is well defined, solution technique for dynamic programming simulation everything is well defined but I cannot apply that technique manually to my water resources problem. There are because of two things. First one is the system is large. The components are large number and also the interaction between the components is complicated. Even with the advent of these computers all these things still we are unable to find out what is the relationship between volume of release from the reservoir and the seepage rate in the canals. Still we assume or we estimate we never calculate. So that is why I still classified this even though solution techniques are well defined we may not be able to do this manually. Even 100 people sit together and do this problem we will not solve a just 20 by 20 linear programming matrix. So I need a software. I need a computer to solve this that is why personally I feel that these techniques are also can be classified under soft computing techniques. I can say this is conventional soft computing techniques and recent tools are modern soft computing techniques. These are all tools. So yesterday I told this story God has created the resource because after creating man he has stopped creating better creature because it is evolutionary. So one better creature has to destroy the previous creature but after that he has stopped but he has created water and asked us to manage technically efficient way, technically effective way and economic way. If we fail in this management this technology will go we will end up with war. So that the better creature created by God will vanish from the world. So I will end up this one.