 So, what I am going to talk today, the first half an hour is the unindicated approach of finite element method remote sensing and geographic information system. So, this was a part of our one of a sponsored project sponsored by ISRO and then this was also a part of one of my PhD student who completed PhD and now working as a faculty in NIT Warangal. So, we will just to see some important aspects about the watershed and how we can do an integrated watershed modeling using finite element method, finite GIS and remote sensing. So, as I mentioned even my first lecture, so say there is of course we will be dealing with surface water and groundwater. So, surface water, groundwater aspects we have already seen like groundwater say we want to assess how much groundwater is available and quality issues and surface water is concerned mainly we will be dealing with say watershed modeling that means you want to assess with respect to rainfall how much runoff and how much storage can take space and then surface water other issues will be like hydrodynamics in rivers, lakes, then coastal areas, sea etc that means coastal water bodies. So, these are the main issues we have to that main problems we have to solve by using the numerical methods like a finite difference and finite element method. So, due to lack of time I will not be going to the surface water issues like river hydrodynamics and lake hydrodynamics some of the aspects already given in the lecture not, but today this just next half an hour we will be discussing how we can do an effective type of modeling for rainfall runoff and runoff estimation using the integrated approach of finite element method and remote sensing and GIS. So, as all of you know that the watershed is the basic unit where we can do say specified activities like water management. So, watershed based model is very important and then as all of you know that there are number of different types of modeling techniques available or modeling procedures available. So, you can see that some of the important modeling procedure include black box model as I mentioned artificial neural network is a black box model then we are having the empirical types models or say lumped models like say a CSCN based models and then the other important class of models are called distributed models. So, distributed model as I mentioned in my earlier lecture it is physically based model and then we are using the fundamental principles the physics of the problem we are dealing and directly we are solving the governing equation with respect to the data available for the particular watershed or particular domain which we are considering. So, the runoff the for the runoff estimation from the rainfall for a particular watershed particular area we need a lot of data and then when we are trying to solve the original governing equations. So, that is what we are trying to do that means with respect to rainfall how much is the runoff taking place. So, we want if you are going to construct a dam or some other structures at particular location we want we can find out how much will be the runoff coming and then how much storage is possible. So, that is the aim of these kinds of modeling. So, the distributed models so, you can see that lot of data are required then of course the modeling is very complex compared to the black box models or the lumped model, but you can see that it really represents what is happening with respect to the real domain. So, that is the advantage and then even though the accuracy may not be so good even compared to the black box model, but it shows what is really happening with respect to the real system. So, that is advantage. So, here as I mentioned we are going to discuss the final term based modeling. So, the governing equations as far as the watershed modeling is concerned here these equations are called Sainte-Vine and equations there is one continuity equation and then one momentary equations I mean in two one dimension and then if it is two dimensions there will be one continuity equation and then two momentary equations. So, generally either we will be doing one-dimensional modeling or two-dimensional modeling for these kinds of problems, three-dimensional model or watershed basis is where it is say nearly impossible since you need a lot of data and then it is a very complex process. So, most of the time we will be dealing with one-dimensional modeling or two-dimensional modeling and then of course you can see that this fundamental equation so, called Sainte-Vine and equations we are having a number of say versions of these equations. That means the simplified versions so, one of the simplified version is called a kinematic wave equation and then another some more complicated equation is called diffusion wave equations. So, in the kinematic wave equation actually the equation is the Sainte-Vine and Sainte-Vine those who know about Sainte-Vine and Sainte-Vine anyway I have not placed here the Sainte-Vine and Sainte-Vine but say it is continuity equation plus the momentary equation. So, the kinematic wave approach means it is simplification to the Sainte-Vine and Sainte-Vine or the dynamic wave form of modeling. So, in the kinematic wave equation we utilize the original the continuity equation and we assume that the best slope is equal to energy slope for the given channel or given the overland flow which we consider. So, that is a simple concept that is a simplified model. So, that is called kinematic wave approach even professor V.P. Singh has written a book and a lot of information are available on this kinematic wave based model since it is a process is so complex. So, this simplified approach is generally used and then the diffusion wave model that is again say it is more complex than kinematic wave approach, but simpler than the original Sainte-Vine and Sainte-Vine equation or the dynamic wave equation. So, here not only a 0 is equal to Sf that means best slope is equal to energy slope but we consider the gradient with respect to that means the say how the energy you know that y plus z is the energy specific energy at any location plus v square by 2g. So, y plus v square by 2g is considered and then its gradient is also considered. So, the governing equation when it comes here we will be discussing about it. And then here as I mentioned watershed is considered you can see that any type of watershed there will be say if I consider a watershed like this a simple watershed I can show you here. So, this is a typical watershed where you can see that all the water will be draining here there may be a river here and then a number of streams may be coming like this. So, here this is a geographical boundary of the watershed. So, whatever water falling this side it will come here and other side it will go like this. So, whenever rainfall occurs you can see that it will be water will be falling on the land and then it will be first joining the small channels and then the small channels will be finally joining to the large river or stream and finally it will go flow like this. So, we are having an overland flow components there will be overland flow and then channel flow. So, two components as far as watershed modeling is concerned one is overland flow that means we do not consider the channel, but what is the other overland flow in these areas and then we will be having the channel flow. So, the channel flow the all the overland flow components will be coming to the channel flow and finally it has to be routed so that we can get at any location where we want to find out how much is the runoff taking place. So, this overland flow we have to consider separately and so in this modeling approach which we are going to discuss we will be considering the overland flow separately and then we will be considering the channel flow separately and then we will be solving these equations based on kinematic wave approach or the diffusion wave approach and then we will be routing the flow through the channel so that we can find out how much will be the runoff and then of course you know that there are number of processes taking place in a watershed with respect to the rainfall there will be infiltration taking place then interception may takes place then say interflow may take place number of hydrologic processes are there in any watershed. So, some of these important process we are considering this model here and like interception and interflow and so by considering all these aspects we have developed a composite model. So, when we consider actually the the rainfall runoff for a small event that means an event may be for few hours so the distributed model when we consider the effect of evaporation if it is considered it is good but that effect will be much much less compared to some of the other important processes like the infiltration interflow interception etc so that evapotransplantation is not considered in the present model since it is a it will be very small percentage of the total losses and then as I mentioned here we are going to discuss say an integrated modeling approach. So, GIS is used for database preparation. So, database means we need to find out what is the say as I mentioned in finite term method preprocessing is there so the end of preprocessing is done using GIS package arc info here. So, it needs so we have to find out the drainage then we have to find out what are the various parameters then we have to prepare the end air say the porosity variation then the land use land cover from that mining's roughness so many parameters we have to get. So, all these things are found the database preparation is done using geography information system and then the remote sensing is used for land use land cover preparation. So, from the land use land cover as Professor E.P. Rao mentioned yesterday you can see that there will be we can prepare the various the roughness or mining roughness and various other parameters from the land use land cover and the model application we have applied a number of as I mentioned in any kind of when you develop a new model we have to verify with available so a hypothesis water shed we utilized for verification purpose and then for different watersheds this model have been applied and then we have found the we have compared with the offset data and then so that we can say we will get the conference to use this model and also a sensitivity analysis has been done with respect to various parameters here. So, here the framework of the modeling approach is shown in this flow chart here. So, if you are going to if you want to model a particular water shed here we are having the water shed so selection of water shed then data collection for the water shed. So, as I mentioned last set of data is new rainfall then we need the porosity we need the saturated hydraulic conductivity like that number of parameters we have to collect. So, data collection for the water shed and then we prepare the thematic maps with the help of say land use land cover map then topo sheet then we have to prepare the digital elevation model map then slope map then drainage map etc. So, this here we utilize the remote sensing data and the geographical information system. And then here say we have selected the finite method as the numerical model. So, for FEM formulation of the model we will be discussing we have already seen how to do the FEM formulation. So, here we have used the Galerkin finite method as we discussed yesterday. So, this can be actually the data collection and data base development and the model development can go in parallel. So, this year you can see in parallel and finally, once the model is ready you can first verify with respect to some analytical solution or any other say the some of the other solution available or the available software you can check how effectively your model is working. So, model verification development and verification. And then you are coming back to your water shed which you are considering. So, there you have to test and then evaluation of the model. So, as I mentioned we have to do a number of calibration processes since we are a large set of data which are not so correctly can be obtained from water shed we assume with respect to either literature value or some field study. So, we have to calibrate the model and then say we have developed a user interface also and then we applied to various water shed. So, here you can see how is our approach. So, as I mentioned for a water shed like this. So, there will be a channel then there will be overland flow. So, here rainfall occurs and then there will be infiltration test space and then some interception losses may test place with respect to any vegetation cover and then interflow you can see that the some of the flow may come back and then that may come back to the channel. So, this is the physically based model this physically based model is developed. So, interception loss is calculated using an interception model called LISAM model. So, this model actually this is described we have cumulative interception during rainfall even this given by this equation where CP is a constant and LAI means land area index and CMACS is given by this equation based upon land area index leaf area index not land area sorry leaf area index LAI how much the vegetation is there accordingly and this is with respect to the rainfall and then some of the parameters. So, this is explained in some of the literature already which is given and then the another important component is so called infiltration model. So, infiltration is one of the major component in any of the water shed modeling especially that affects a lot with respect to the runoff. So, the two infiltration models we have tried here for first one is called Green Ants model and second one is called Phillip model. So, Phillip infiltration model say for example, we calculate the infiltration right and subsequent excess rainfall by using the rate of infiltration given by this equation where SI means see initial soil moisture and K is the hydraulic saturated hydraulic conductivity and T is the time. So, this infiltration this SI is the infiltration subjectivity given by this equation and SI NI is the initial soil moisture and this KS SI and ETA are some of the important parameters which we have to which we can obtain for the type of soil directly for the given system. So, we used these two types of infiltration model and then of course, the other important component is the overland flow. So, as I mentioned we are we are used two types of model one is the kinematic wave model kinematic wave form and second one is the diffusion wave form. So, the continuity equation is same see here the basically we are using a one dimensional model. So, the continuity equation is given by del Q by del X plus del H by del T is equal to RE where RE is the effective rainfall and then H is the flow depth is the time Q is the flow per unit width flow rate. So, this is the continuity equation and then the simplified form of the momentary equation that is the St. Mayans equation which is the dynamic wave form. So, that is simplified to two terms one is kinematic wave form where S0 is equal to Sf that means the bed slope of the channel or the overland area we are considering that is equal to the energy slope and diffusion wave form as I mentioned del H by del X is equal to S0 minus Sf. So, these two forms so, first model kinematic wave based model. So, this equation S0 is equal to Sf plus this equation will be solved and the diffusion wave form will be solving the continuity equation and this second form of the equation. So, now as I mentioned here we use the Galerkin finite element method. So, you have to solve this equation effectively the continuity equation with by using this S0 is equal to Sf or the second equation. So, you can utilize as we have seen we have used the here method of Aeterosudel and then we use the Galerkin criteria. So, here one dimensional form of the element is used. So, actually you can see that we consider here as a strip this is one strip. So, here this is a strip wise only it is a one dimensional model which we are considering. So, you can see that instead of going for two dimensional model actually two dimensional model is better, but it is very complex since you have to get a lot of that you can see that wherever at different location the slopes then how the the geographic is changing it is very difficult to account. So, for the time being what we did we consider this as a one strip is coming here another strip is joining another strip. So, it is actually a strip wise modeling is done for watershed here. So, this is another strip coming. So, all this strip wise. So, this strip means actually it is considered as a one dimensional flow and then with respect to effective rainfall it is joining to the channel here. So, different strips are joining to the channel and channel is also considered as a one dimensional flow finally, we are finding how much is the discharge coming here and at different locations also we can find out. So, this is the basic principle which we utilized here. So, the kinematic waveform is given here diffusion waveform is given here and correspondingly we can get the Galerkin finite element formulation. So, you can just first integrate and then use their shape function and then you can do one integration by parts and all those procedure which we have seen yesterday. So, that you have been used only the final equation is given here and for when we are using diffusion wave model this approximation is used here. That means, at different location from S k minus H i by L that between two nodes if you consider two nodes here one location to another location. So, that is divided by L that gives this equation. So, that is what is done for the overland flow model and then next component is the channel flow. So, the channel flow is considered as I mentioned here you can see that all these overland flows are joining at different locations to the channel. So, this channel is also considered as one dimensional flow. So, the given equation is del Q by del x plus del A by del t minus Q is equal to 0 where Q is the flow in the channel A is the area cross section for the channel and Q is the whatever is adding that means coming from different location. That means, this you can see that overland flow is joining at different location of the channel. So, that is what is this equation and then of course, the momentum equation is the simplified form of the momentum equation like kinematic waveform and the diffusion waveform are used here and then this Q is calculated using Manning's equations 1 by N R to the power 2 by 30 this equation is used for the but here this is the energy slope you know that since this is a gradually varied flow and this is the disturbed equation which is utilized here. So, then correspondingly we write the finite element formation. So, this is the basic equation which we are utilizing for developing the numerical model and then corresponding finite element formulation is given here. Actually, this is published in the this formulation and application is published in the general hydrologic process and water source management to international journals. So, entire formulation and their applications are available in those journal that is in 2007 issues. So, then this channel flow is given and then of course, you can see that another component is so called the inter flow component. So, inter flow component is here it is defined by the continuity equation del Q i by del x plus eta del h by del t is equal to i i. So, where Q i is expressed by Darcy's law. So, this is eta is a one component and then this is with respect to the infiltration rate how much is coming back to a system. So, that is done the inter flow equation and then this also developed using a finite element formulation given like this using the Gaderkin finite element method. So, now you can see that a number of components like interception inter flow then overland flow channel flow then say we are combining together. So, at any location if you want to find out what is the flow taking place with respect to given rainfall how much is runoff is taking place that is what we want to find out here. So, that is the way which we have developed this model. So, this shows the flow chart for the model you can see that we start with a large set of data input like excess rainfall infiltration data then number and size of elements. So, this is all preprocessing and then calculation of element matrix for channel and overland flow then the finite element procedure you can see that the we will be finding the flow depth at different locations and then an iterative process. So, this is the this is essentially the flow chart for this model which we have developed. And then now we as I mentioned once the model is developed we have to first verify with some of the available solutions. So, actually this model there is some analytical solutions available only for overland flow this is not a complex flow like what is there, but some analytical solutions are available in literature whereas, typical rectangle domain is considered and then typical rainfall pattern is considered and then how with respect to that these are all the influence matrix for the finite element method you can see in that lecture notes that means, for first we write elements we have seen first we apply for one element. So, that element says some part A X is equal to B that type of that A correspondingly A this all these components will be added up and finally, a final matrix will be obtained. It is not a C is not an input it is mathematically this thing. So, mathematically when we integrate actually you can see some in that lecture note some formulation is given. So, here we have verified with respect to an analytical solution available in literature and then we found that our model is working perfectly within 1 or 2 percent difference only is there, but whenever so, mathematically or numerically the model is right. So, that gives the gives the confidence your model is working fine, but if the data available is not right or the data accuracy is not good then it will be the prediction may not be good. So, what why we are looking for an analytical solution and whether your model is working fine the reason is that you to you get a confidence as my model is working fine and the if somebody is given data if the data is not accurate then I cannot help you see that in the rainfall or not modeling depends upon how accurately you are measuring the rainfall and then number of other data set like soil moisture then like porosity that is in the large set of data which we have to utilize. So, depending upon the accuracy of the data only your model will be predicting. So, but to show that your model is working fine you can use a simple case like analytical solution which is already available in literature and then we verify and then for this model we got about 99 percent accuracy. So, that way we have shown that the model is working and you can see that when I coming to the runoff modeling the accuracy is not so good. So, even in the international experts open that yes it may be due to the data problem. So, this model which we have discussed here we have a series of model first one is so called. So, depending upon the infiltration model we can have different types of models. So, this is kinematic gamma diffusion gamma kinematic phillip diffusion phillip like that a number of models were developed and then with or without interception. So, it depends upon how much data is available for the given type of given watershed. So, this has been applied for different watershed one watershed in cat soap that is in Netherlands. So, a good data set was available. So, that is why we applied for this watershed and then we applied to another watershed in US where data collection and modeling is going on for last few years and then three four watersheds in India also we have applied this model one of the Indian watershed will be discussing in detail. First let us see one of the watershed which we did for the Netherlands watershed. So, this watershed is located in South Limboon Netherlands area is about 41.56 hectares this is a basically an agriculture watershed and the mean annual precipitation 675 millimeter and altitude is varying from 80 to 110 and slope is gentle to moderate and soil class is silty long and land use winter wheat sugar beet and potatoes. So, here this data is obtained from professor Victor Jettin of this University Woodridge University. So, as I mentioned here you can see this is the watershed. So, there is a stream coming you can see that there is a stream like this and these are the overland flow coming. So, we consider different strips joining and then this is the outlet of the watershed with respect to the final tournament modeling. So, there are a series of procedure like first we have to generate the map and then. So, we got some data from them and then we use the arc info GIS package and the mining reference maps based on land use prepared final tournament grid map. So, element of length 50 meters have been considered in this modeling and grid has map has been overlaid on slope and mining reference maps. So, that a combination is obtained and mean value of slope and mining reference each element of the grid and nodal values average of adjacent element values. So, this is the watershed and this is the discretization you can see these are all different strips joining the stream. So, this is the way which we considered. So, actually the overland flow is also one dimensional model and the stream also one dimensional model. So, here for model simulation we considered say 10 rainfall events and we calibrated as I mentioned last set of data we know only some average way the data set. So, we had to calibrate. So, we used the 5 rainfall events for calibration and 5 were used for validation. So, the channel parameters like a channel width is 4.4 meters, slope is 0.02, mining reference 0.23 etcetera have been used and time step is considered 30 seconds and calibration is done by altering the values. So, here actually one of the important aspect here is this so called the infiltration. So, infiltration parameter you see that it is going to the soil. So, it is very difficult to find out some of the important parameters. So, we need a thorough calibration is required and depending upon how accurately you can do this the model performance will be better. So, by altering the values of infiltration parameters by trial and error or you can do one optimization techniques on the best visual fit of the hydrographs the model fit based on difference between the observed and computer runoff volume runoff peak runoff and time to pick. So, this were the criteria which used for calibration and validation is with average. So, 5 events we used these collaborations and from that we got the data. So, average of that is used for the validation purpose and then also we compare the results available using some other numerical methods also. So, here this shows some of the events you can see that this black this shows the rainfall all this rainfall and then here you can see the runoff. So, this is in time. So, about up to 400 minutes or 300 minutes it is simulated and this is discharge meter cube per second on the y axis. So, here the this red color or this color shows the offset and the black color shows the simulated. So, these are for the calibrated events. So, you can see that as I mentioned. So, this say the model you cannot blame since we have only verified 99 percent accurate is which is working for the available analytical solutions, but when we come here. So, how the performance of your model depends upon how accurately you can get the data. So, the accuracy of the data is not good, then the model will not perform good. So, we cannot blame the model. So, we it depends upon how accurately you can get the data. So, this is the way which we could calibrate, but it may be better if you get more accurate data from the field and then of course, we validated some of the events actually you can see some of the things are working fine like a peak runoff and time to peak, but some of these things are not working fine especially here the in this particular model. So, this is not a continuous simulation model. So, you can see that there is split of the the rainfall. So, this rainfall is up to this and then there is a spring that is why the model is not capturing appropriately when it goes for validation, but say the error is about to 20 to 30 percent, but so this kind of distributed model if you go to literature this much is allowed. That means, why allowed is the data is very difficult to get and their data set, but it gives how the system is behaving with respect to time. And then say when we consider when we are going to construct a dam or when you are going for flood management measures this kinds of results are very useful. So, that is why these kinds of models which we are doing. So, this is the problem, but if you may say that if I do a black box model like N and or if I do a lambda model the results may be better, but then the difficulty is that you cannot get to these kinds of pattern or that means, say how is what is really happening with respect to the physical process it is very difficult. So, here this data this table shows how with respect to various events calibration stones, validation stones, how the variations with respect to volume of runoff peak, runoff time to peak all these results are listed here. So, we compare with other models also. So, this is not only a problem for our model, but say the what is available literature also our model performed better than what is available in literature. So, the difficulties are as I mentioned it is to get the correct set of data input data for the modeling. And so, here as I mentioned the variation is some results are very good some results say as I mentioned some places even it may be more than 100 percent or 150 percent. The reason is that that for this model it is basically what is with respect to rainfall immediately how the runoff is taking place is what is that is predicting. But if there is an intermittent rainfall taking place then also there is a problem with respect to this model that is why some of these changes which we can observe here. Then we did a sensitivity analysis with respect to as I mentioned most sensitivity parameters are with respect to infiltration parameters here. So, that is like saturated hydraulic conductivity, initial soil moisture, then porosity etcetera. So, as for academic interest we just varied this parameters 5 percent, 10 percent, 20 percent etcetera and then we just identified what is the most important parameter. So, it was seen that this saturated hydraulic conductivity one of the most important parameter in this kind of model. And then also we did some variation with respect to grid and then variation with respect to time the sensitivity and then we checked how the system is working it is distilled here. So, with respect to grid variation the percentage variation is 8 to 10, but you should have reasonable grid it is I am not saying that it is not the model is of course, grid dependent, but you should have reasonable grid, but no need to go for a very final mesh. Since very final mesh the computation will be very very to time consuming and data preparation also will be time consuming. And time step variation also a small variation is there, but here we have used a 30 seconds. So, that too seems to be a very good for this model. So, this shows the sensitivity with respect to various parameters. So, here the saturated hydraulic conductivity which is affecting the the so the infiltration process that is one of the most important parameter in this model. And then this shows the here the results of Harsol watershed this is a watershed in in Maharashtra near Nasik. So, the area is about 10.11 square kilometer and here the data of course, this data is a major issue. So, you can see that now in most of the states a project called hydrology project is going on that is supported by UNESCO and say UNO and World Bank UNESCO and World Bank. So, this project actually the purpose is that to collect large set of data about various river basins and then that can be say check the variety of the data and correct it appropriately and then may make available for the the researchers or the field engineers. But what we observed here also even this this data what we got is actually from an Indo-German project. So, that data reliability is much much better, but what we observed what is available in this hydrology project is also not so good. So, depending upon data availability the the model behavior will be there and then the remote sense remotely sense data of IRS 1D list 3 image of January 1998 has been used for this Harsol watershed modeling and thematic map like drainage slope land use land cover prepared. So, this shows the drainage map of the Harsol watershed there is a major stream going like this. So, we consider it as a major stream and other minor streams are accounted with respect to the overland flow and here this is the outlet of the watershed. So, this shows a photograph of the watershed. So, this is the stream with the main stream passing through with respect to the watershed and this shows the digital elevation model and this shows the slope map. So, we use dark info with respect to the topo sheet and then the data available from the satellite imagery. So, that was we used to prepare this digital elevation map. So, this shows some more data from the field field and here the farce color composite and land use land cover map used for the this particular watershed Harsol watershed for the digital elevation model and land use land cover preparation. So, this shows some of the field in this watershed. So, my research always collecting some data. So, this watershed we discretized we actually as I mentioned this is the major stream here and then this also one-dimensional modeling is done. So, you can see that number of strips joining with respect to actually the strips are decided according to the topography of the area. So, that is coming and joining the stream. So, overland flow note 188 channel flow elements 22 and channel flow length 250 meters is considered here and average bed width is 18 meter and slope we consider with respect to overland channel flow and manning's roughness obtained from the roughness map which I have shown earlier. So, here also we calibrated since the data of it is a major issue for this kinds of modeling as I mentioned we calibrated for three rainfall events and then validation is done for two rainfall events. So, these are some of the parameters like saturated hydraulic conductivity and suction head and saturated water condense then initial water content. So, these are the calibrated parameters for this Harsol watershed. So, this shows the calibration of the this is the rainfall and this shows the the runoff with respect to time. So, for three events and then this is for the validation events actually for this watershed the model is working much better and the results are compared and volume of runoff peak runoff time to peak runoff are shown here for various calibrated events and violated events. So, this is the way as I mentioned this is a very complex process. So, already this part of sponsor project as well as as I mentioned already one student got a PhD. So, the the complexity of this kinds of model is say it is very difficult to deal especially data availability and then when you put it into a framework of numerical model like finite element method and data based urban GIS it is a very difficult task. So, here we are there by an integrated watershed model using finite element method geography information system and remote sensing technique and here two infiltration models Philips and Gamal models have been used and this model has been applied to a number of watersheds. And as I mentioned the validity of the verification of the model is done with respect to some analytical solutions. So, we are we have made we have it is we assured that the model is working perfectly ok, but only the major issue here is the the data sets and then also we conducted a sensitivity analysis various with respect to various parameters. So, the most sensitive parameters we what we found was such that hydraulic conductivity and that is very difficult to obtain in the field also. And then second one is the initial soil moisture and say we also did study with respect to the grid size time step except by how the system will be behaving. So, this is just in an actual how we can do. So, as I mentioned this is a very complex topic. So, I have just taken 30 40 minutes to explain to you how such a model can take place. So, five minutes we will have a brief discussion before going to the next topic. If you have got any questions you can ask now. So, you mean the before starting. Yeah. So, this is actually that is what I am saying say some of these infiltration parameters basically depends upon what is the previous rainfall and those parameters. So, that is why actually it is very difficult to you see that in field level it is collecting the data is so tedious. So, what we did? So, that is why this collaboration we collaborated with more events and to get a how the watershed behave with respect to this data. So, if 10 events are available 5 or 6 events we calibrate for various parameters then we try to validate the model. So, that is very important questions. But now I hear that in US some watersheds they it is small watershed experiment based watershed they can they put some crops online. So, that all the time when rainfall they express immediately the data is coming and collecting and then immediately you can have very good model. But the difficulty understand this is so these kinds of important parameters to collect from the field is so tedious. So, but that is why the model is not showing that 70 percent 80 percent accuracy is good enough and our main purpose is qualitatively fine with respect to time how much is the runoff possibility how the flooding takes place all these things are given by this kinds of model. But that you will get a very good accuracy maybe 95 percent accuracy using ANN models. But that is based upon only inflow and outflow nothing more than that you are not considering what is really happening in the watershed. So, you are not getting a touch of or you are not getting a feeling of the physical process taking place in watershed. So, that is why still we are doing even though it is so complex and whenever we are sending such a papers to a journal they may also ask, but now we have already published 2-3 papers based on this work. So, the reason is that that is the difficulty and I am happy to say that even if I get 70 or 80 percent accuracy that is good enough. So, this as your question is this is done through calibration. Any other question? All events are of different shape and size. Yeah, of course as I mentioned this is we do a one-dimensional say strip type and then you can see that say accordingly you say we are having the top of sheet we are having the DEM detailed elevation model. So, with respect to detailed elevation you know you can have a an understanding of how the real system is. Accordingly only we have changed the shape and we have put the slope and with respect to slope also we changed the shape. So, the shape is with respect to detailed elevation model slope map and then the top of sheet or the realistic conditions are available in the field. So, that is why different shapes of elements actually it is only one dimensional strip strip type element, but width may vary size may vary.