 Namaste and welcome back to the video course on watershed management. In module number 4, watershed modeling today lecture number 16, we will discuss hydrologic modeling. So, some of the important topics covered in today's lecture include rainfall runoff modeling, runoff process, physical modeling, distributed model, then some of the important keywords for today's lecture include rainfall runoff modeling, physical modeling and distributed model. So, as we discussed earlier, so when say we deal with the water resources for a watershed, so we have to see the various processes what is happening for the transformation from rainfall to runoff or the precipitation to runoff. So, we have already seen that various hydrological processes will be there between this transformation from precipitation to runoff. So, some of the important hydrologic processes which we have already seen earlier is say the interception by the vegetation and then say evapotranspiration, then surface storage or depression storage, then the infiltration, then interflow percolation and then surface runoff and finally, coming back to the direct runoff and then all this direct runoff from the as overland flow runoff it will be joined to the channel. Say for example, this is the watershed, then you can see that from various small small channels finally, a big stream for the watershed and the runoff will be taking place through the channel to the outlet of the watershed. So, here also we may have to include the ground water storage, ground water processes. So, mainly the surface water processes and the ground water processes and surface water processes we can classify into the overland flow components and the channel flow components. And then when we are looking for the hydrologic modeling, so we have to assess for the given rainfall condition how much will be the runoff at any location of the watershed, say either the distributed way or as a lumbered way at the outlet of the watershed. So, generally say at the outlet of the watershed we will be describing as say in terms of a hydrograph. So, where the hydrograph is the discharge versus time, so you can see that say if this one is the given rainfall say a millimeter per hour and then correspondingly we can identify how much will be the runoff as the hydrograph discharge versus time. So, at the outlet of the watershed or in the case of distributed model at any location of the watershed. So, that way as we discussed earlier, so we have a various components as far as within the transformation from the rainfall to runoff. So, we have already seen how to construct a watershed model in the previous lectures. So, we have to say first we have to develop a conceptual model for the watersheds including watershed delineation and the consideration of various parameters and then we have to formulate the model. So, it can be either lumped model or the black box model or the distributed model. So, that aspect also we have seen in the last lecture. So, then once the model is formulated or we have to develop the corresponding model as a computer model or the otherwise an analytical model and then say for the given problem or for the given area we have to calibrate various parameters as far as the watershed disconsent. And then for the given conditions say for the given intensity of rainfall or for given the event based rainfall conditions either for event based simulation or continuous simulation we can do as far as the rainfall to runoff modeling say as a watershed model is consents. So, in all this aspect as we have already discussed there is an input function. So, input function is mainly the rainfall as far as the watershed disconsent and then output function is the runoff. So, runoff taking place at the outlet or at any location of the watershed and transformation function is the third one and that is the mainly the various hydrological processes taking place between the rainfall to runoff. So, as we already discussed so say as far as surface runoff is consents. So, when the rainfall is taking place same we can classify as far as runoff rainfall runoff is consents we can classify as the surface runoff into overland flow and the channel flow. So, after the losses or the all the transformations taking place then we can see that to the overland flow the say on the overland flow the runoff starts and then through small small channel it will be coming to the main channel and then the channel flow is taking place. So, when we say that say when we are going to model in watershed as far as rainfall runoff is consents. So, we will be we have to consider various processes as we so called transformation taking place and then we have to also consider the ground water come flow come on see if it is there and then as far as surface flow is consents we model for the overland flow and the channel flow. So, both this should be combined together to get the runoff at any location of the watershed or the outlet of the watershed. So, now we will see more aspects as far as the hydrologic modeling is consents. So, we have seen the various classifications of the different types of models and different kinds of concept wise we have seen the last lecture. So, now in today's lecture we will be discussing about the deterministic hydrologic modeling. So, here say depending upon the parameter considered for the watershed we can classify into three main categories. So, first one is the the lumped model, second one is a semi-distributed model and the distributed model. So, this classification is mainly based upon how we consider the various parameters. So, first one is the lumped model. So, lumped model is consents. So, when we are discussing a particular watershed like this. So, if this is our watershed which we are considering. So, you can see that. So, here say as far as the watershed is consents. So, we have to see the various parameters which are consented here say like the porosity or various other parameters like any or the saturated hydrologic conductivity like that various parameter will be lumping for the total watershed as a single parameter. So, that process is called a lumped model. So, when we are discussing for the given rainfall condition for the areas consents there will be say one value for the total watershed. So, that is so called a lumped model. So, in the lumped model we consider the parameters say which we are which are not varying especially within the basing and response is evaluated only at the outlets. So, the parameters variation we are not considering, but so the parameters lumped for the total watershed as a single parameter. And then this is without explicitly accounting for the response of individual sub basins. So, you can see that. So, here you can see that the various sub basins we can consider for this watershed this may be different sub basin for the considered watershed. So, here we are not considering the variations as far as this sub basins are consents. So, but here the parameters say we lump for the total watershed. So, here the parameters do not represent physical features of the hydrologic processes. Model parameters are the parameters which are area weighted. So, it is an average for the say if the various parameters for sub basins are known. So, we consider say the average of those parameters and then we lump for the total watershed. So, that way when we are doing this kinds of lump when you are using the lumped models. So, it is difficult to cope up with the event-based say rainfall to runoff modeling, but we can do continuous simulation say for a daily basis or weekly basis or a monthly basis what is happening since most of the parameters here are lumped. So, generally for the when we use lumped models the discharge is the discharge prediction is only at the outlets and then. So, that way we may not be able to identify what is really happening with respect to spatially or with respect to time, what are the various hydrologic processes how this process are varying we may not be able to identify when we use the lumped models. But of course, this lumped models how got a number of advantages. So, as I have listed here this models are very simple and then minimal data requirements and then easy use. So, say since the parameters are lumped average parameter we are taking. So, that way the modeling is very simple and data requirement is very less and the model development and running and getting results are much easier. But of course, the some of the disadvantages like this models the lumped models we know truly represents the various hydrological processes taking place within the watershed. So, that way we may not be able to capture what is happening with respect to the rainfall to runoff various things happening and then how the runoff is distributed throughout the watershed all those things we may not be able to capture as far as the lumped models are concerned. So, there are number of lumped models available. So, we have already discussed in the last lecture about the soil conservation current number based model. So, that is one of the commonly used lumped model for watershed modeling then other softwares like IHA, CRES, IHCRAS then water balance water balance model etc. So, these are some of the lumped models commonly used in practice. So, that is one category of models. So, we have already seen the advantages and limitations of lumped models. So, now if you want to identify what is truly happening within a watershed we have to go for a either semi-distributed models or fully distributed models. In the case of semi-distributed model the parameters are partially allowed to vary in space by dividing the basin into number of small sub basins. So, here say you can see that if this is our watershed which we consider. So, then we can say if this is the channel then various sub basins we can identify for the watershed. So, this is basin 1, 2, 3, 4 like that. So, various sub basins depending upon the say for example, say the land use, land cover. So, like that. So, we can classify various say sub basins for the given watershed and for each sub basins we can identify the various parameters which are we are directly dealing with for that particular model. So, that sub basin wise actually it is lumped or we are taking the weighted average. So, that way actually to certain extent the various parameters variation will be represented within the watershed, but not to the fully extend like a fully distributed model. So, here the parameters are partially allowed to vary in space by dividing the basin into number of small sub basin as shown in this figure and there are mainly two types of say semi-distributed models. So, here the kinematic wave theory based models. So, like example is HEC HMS models and then simplified version of surface flow equations or these are all actually simplified version of surface flow equations of physically based model. So, there are we can semi-distributed models are concerned we there can be two types of models one is the say actually it is distributed from the distributed model based upon the Saint-Vinand's equation. So, that is so called kinematic wave theory based model. So, here same the important parameters in this kinematic wave theory models we obtain from the say we take it for the sub basins and then we do do the modeling and second category is so called a probability distributed models. So, probability distributed model the the spatial resolution is accounted for by using the probability distribution of input parameters across the basin. So, the here say instead of say for the given sub-basin also or say for the watershed also we can identify how the the parameters are varying say according to some probability distribution like a normal distribution or any kind of probability distribution which is suitable for that parameter and then say we can take that distribution. So, that distribution so, when we use that kind of modeling so, that is so called probability distributed models. So, here probability distributed models the the some of the advantages like the the it is the structure is more physically based than lambo model. So, then say here the less demanding on input data than distributed model. So, here here the the parameters say compared to a fully distributed model for the semi-distributed model the parameters say the variation is considered. So, that some of the important features of the the watersheds are captured. So, here less demanding on input data than distributed model. So, some of the advantages are like the features are somewhat represented and these parameters are the the not fully like compared to fully distributed model here it is not complete variation is not taken care, but sub-basin based variation is taken care. So, there are number of semi-distributed model available in literature like an same SWMO model same storm water management model then HEC hydraulic engineering center hydrologic modeling simulation HEC HMS model and TOAAP model then soil water assessment tool SWAT model. So, all these are somewhat semi-distributed models. So, here you can see that say we consider say for example SWAT model we consider the hydrologic response unit and for each response unit we take the average weighted average parameters and then accordingly the modeling is done. So, that is that category of modeling is called a semi-distributed model and then the next category modeling models are called distributed models. So, here the parameters are fully allowed to vary in space at a resolution chosen by the user. So, here the parameters are varying say according to the realities or how much data we can collect for the watersheds. So, accordingly the parameters variation can be taken care and then we attempt to incorporate data considering the spatial distribution of parameter variation together with computational algorithms. So, we can even this variation we can represent in terms of like some algorithms or some equations for example infiltration is concerned. So, for that how the variation is taking place with respect to soil or with respect to the depth of soil. So, like that we can have various computational algorithms and so actually these are truly the physical models which is representing the complete features of the watersheds, but the some of the disbanded disbanded of these kinds of modeling would require large amount of data we need to capture the entire variations of the various parameters within the watersheds either through field investigations or through some kind of equations and then say some the advantages include the governing physical process are modeled in detail. So, all the aspects we can capture and then results at any location and at any time. So, when we are dealing time dependent modeling. So, the spatial variation we can take obtained say from rainfall to runoff. So, how much is runoff at particular location or what is the depth of flow or how the discharge variation is taking place. So, location and time base we can identify and then say the if all the datas are available in an accurate way I mean the data is accurate then the results will be also accurate. So, highest accuracy in the rainfall runoff modeling is possible. But most of the time this is a big question mark since most of the time say as far as a watershed is concerned many of the parameters are varying drastically from one location to another location. So, accordingly it is very difficult to get all this parameter variations and then say to get the accurate data as far as the parameters are concerned it is not so easy. So, that way the accuracy of the model results will not be to the expected level. So, there will be lot of variation since the data input if it is not accurate then obviously results will not be also accurate. And then some other limitation like high computation time when we are going to run such models we need to run the computer for a long time and then the modeling will be cumbersome then say that kind of models only experts can do. So, that means say those who know what is really the how the modeling is done and then most of the time we have to go for numerical modeling like a final difference or final term in modeling. So, the experts only can easily do this kinds of modeling. So, some of the available software included like a hydrotel modeling mic 11 or mic C models then a Watt flood model etcetera. So, these are all physically based model where we solve the Sainte-Vinand's equations or the Gaviani equations by considering the conservation of mask or continuity equation and then momentary equations. And then we use a numerical tool like a final difference method or final term and methods. And then we develop this model by considering the various hydrologic processes like infiltration, evapotranspiration, interception, interflow, ground water flow component etcetera and then we make this model. So, as you can see so much of data is required to get accurate results for these kinds of models. So, now we will come back to the physically based watershed model. So, based upon the Gaviani equations and the within a based upon a system approach. So, the main aim in physically based deterministic modeling is to gain better understanding of hydrologic phenomena operating in a watershed and how changes in watershed may affect this phenomena. So, this is what we are trying to do as far as watershed modeling is concerned. So, we want to understand the hydrologic phenomena operating and then if any changes are proposed like we are constructing a check dam at particular location or we are going for water harvesting measures then what will happen. So, that way that is our aim. So, as we can see that all the variations or all the topography or the topological features or geological features of the watershed is concerned is so complex. So, accordingly this modeling also very complex. So, only thing is that we can using certain assumptions we can may go for a 1 dimensional, 2 dimensional modeling or we can lambda various parameters or processes with respect to space and time and then we can simplify the models. So, most of the physically based deterministic models generally follow the laws of physics. So, that means mainly in this kinds of models according to the fluid mechanics theories we use conservation of mass, conservation of momentum and conservation of energy principles. After this generally we use conservation of mass and conservation of momentum. So, conservation of mass correspondingly continuity equation and conservation of momentum corresponding equation of motion and then equation of energy or Bernoulli's theorem we can utilize and one or more of this laws and several empirical relations are used in physical model development. So, generally as far as the modeling is concerned we use this governing equations, but to deal with various hydrological processes between I mean the transformation functions like evaporation, evapotranspiration, then interception, then infiltration etcetera. So, various hydrological processes to be considered. So, that way we may have to combine various empirical relations with this physical model or the models based upon the laws of physics. So, finally, as we have seen in the previous slides these kinds of models may be fully distributed if all the parameters variations are considered in a better way as far as the watershed is concerned or it may be semi-distributed models depending upon the way which we consider the parameter distribution or parameter variations within the watershed. So, as I mentioned so, the scope of physical modeling is so, we want to identify what is happening say for example, rainfall to runoff. So, that means occurrence movements, distribution and storage of water and their variability in space and time. So, that is what we are trying to do as far as any hydrologic modeling is concerned. So, rainfall occurrence and then how the runoff movement is taking place and how it is distributed and then what kind of storage is taking place in between. So, all those things we are taking we are studying or we are analyzing with respect to space and time. So, then the as far as the technology of physical modeling is concerned. So, as we have already seen we are solving these governing equations. So, these governing equations are partial differential equations, then say single order, but the it is non-linear type of equations. So, we have to go for numerical modeling. So, this hydrodynamics models we have to develop based upon these governing equations and so, these are physical based on hydraulic models. So, like a dynamic wave model for overland flow then same as we have seen we can consider the overland and channel separately. So, overland flow and channel flow by continuity equation and the momentary equation. So, as far as modeling is concerned even though the physical phenomena is three-dimensional nature depending upon the problem which we are solving. So, we can make into either a one-dimensional or two-dimensional approach depending upon the problem. So, say depending upon the requirements for which we are trying to develop the model and then the data availability we can go for one-dimensional model or two-dimensional model or in certain cases of course, it is quite cumbersome, but three-dimensional model also sometimes we may do as far as the water shed modeling is concerned. So, now, we will come back to the governing equations what are the governing equations like as we have already seen the the loss of physics like conservation of mass and momentum we are utilizing as far as the physically based model development is concerned. So, actually these governing equations were derived in the 19th century itself by Saint-Vinand. So, here we will not discuss the derivation of these equations derivations of the equations in standard fluid mechanics or water shed based books you can see the derivations. So, here we have discussed only the governing equations. So, here Saint-Vinand in 1871 derived this equation based upon the fundamental loss of continuity and conservation of momentum. So, the continuity equation we can write as del a by del t plus del v a by del x minus q is equal to 0 where a is the the the area which we consider and v is the flow velocity and q is the say for example, any inflow or some abstraction taking place within that particular system is consents. And then this is the continuity equation and then momentum equation we consider say del q by del t plus del v q by del x plus g a into del y by del x minus s 0 plus s f is equal to 0. So, this is the momentum equation. So, here q is the discharge say at any particular location which we consider then v is the flow velocity and then g is the accession due to gravity a is the area of cross section or the flow section which we consider y is the depth of flow a series s 0 is the bed slope s f is the energy slope. So, now these are the fundamental equations so called Saint-Vinand equations continuity equation and momentum equations. So, when we solve this so this equations you can see that this is presently it is given in one dimension. So, if this is the water shed which we consider. So, if the main channel and then various say overland is concerned we can consider as various strips or various planes joining to the main channel and then the it can be also considered overland flow also can be considered one dimensional and the channel flow also can be considered as one dimensional. So, when we are solving this the both equation completely like in the continuity and momentum equation then that kind of models are called dynamic wave modeling. So, this is entire both equations are considered then we call it as dynamic wave and then when we are not considering the time dependent time in the momentum equation this time del cube by del t then that kind of models are called quasi-steady dynamic wave models and but of course, this will be solved with the continuity equation and then when we are considering when we are neglecting these two times only up to these times are considered in the as the momentum equation is concerned then we call that kind of model diffusion wave model. So, this time in this equation and plus the continuity equation. So, that is how called diffusion wave modeling and the kinematic wave model continuity equation and we consider this bed slope is equal to energy slope. So, that kind of models are called a kinematic wave model. So, this physically based models we can classify into dynamic wave model quasi-steady dynamic wave model or diffusion wave model and the kinematic wave models. These Saint-Venant's the equations developed by Saint-Venant's are based upon certain assumptions. So, the assumptions I have listed here. So, in this modeling in the the governing equations are based upon that the flow is one dimensional and then hydrostatic pressures prevails and vertical accelerations are negligible and streamline curvature is small, bottom slope of the channel is small, steady uniform flow equations such as Manning's or Chase's equation can be used to describe the resistance effects or the frictional effects then the fluid is incompressible. So, these equations are based upon the these assumptions. So, the governing equation as I mentioned in the previous slides are one dimension nature. So, as you can see that here if this is the main channel for the watershed then you can see that we consider as one dimensional flow and then the overland flow is concerned we consider as triplo joining the main channels as one dimensional. If you critically analyze this Saint-Venant's equations you can see that different forms of these equations especially momentary equations we can write in different forms say either in terms of velocity only or in terms of discharge only as shown in these two equations. So, if you critically analyze this equation you can see that this term 1 by A del Q by del t or del V by del t this is so called a local acceleration term and then this term which is V into del V by del x or 1 by A del by del x or Q square by A this is so called a convective acceleration term then this term is so called pressure force term and then we are having the gravity force term. So, here this SF is the frictional force term. So, as I mentioned we can have a kinematic waveform or diffusion waveform or dynamic waveform and if it is steady state we can have steady dynamic waveform also by neglecting the variations of this del V by del t or this term local acceleration can be neglected. So, now the Saint-Venant's equations are concerned and say as I mentioned we can have various forms like kinematic waveform or diffusion waveform or dynamic waveform. So, when the gravity forces when the kinematic wave is formed when gravity forces and the friction forces balance each other like say for example, steep slope channels with no backwater effects. So, then that kind of modeling is called a kinematic wave model and diffusion wave model we can use when pressure forces are important in addition to gravity and frictional forces. So, that kind of say model is diffusion wave then dynamic wave is when both inertial and pressure forces are important and backwater effects are not negligible like mild slope channels and downstream control with the downstream control. So, that way we may have to use the dynamic wave model. So, depending upon the problem we can choose either the full dynamic waveform like the full Saint-Venant's equations or we can go for the diffusion waveform depending upon the condition the channel condition or the depending upon the problem or we can go for the kinematic waveform. So, accordingly we can choose the model. So, what we have discussed is the Saint-Venant's equation in its general form. So, as I mentioned we are having the continuity equation based upon the conservation of mass and then equation of motion based upon the conservation of momentum. So, as far as these equations are concerned we can rate either in two dimensions or one dimensions most of the time either 2D or 1D equations will be utilized. So, these equations different forms like conservative form or non conservative form different forms we can write depending upon the wave which we consider. So, now we will consider this Saint-Venant's equations for the overland flow and channel flow separately. Since, when we go for watershed model as I mentioned we may have to consider the variation of the all the from the rainfall to runoff with respect to the the overland flow and the channel flow. So, now let us see how we go for overland flow. So, the Saint-Venant's equation continuity equation in two dimension we can write in this form where del by del x of u bar h plus del by del y of v bar h plus del by del t of h is equal to r e where r e is the rainfall excess. So, r i is the rainfall then and f i is the infiltration and taking place. So, r e we can get the excess rainfall. So, this will be equal to r e. So, where u bar and v bar the velocity in x and y direction h is the depth of flow and x and y are the the dimensions in x in x direction y direction and t is the time. So, then correspondingly as far as overland flow is concerned the moment equation two dimension we can write in this form del u bar by del t plus u bar by into del u by by del x plus v bar del u bar by del y plus g into del h by del x minus g into s o x minus s f x plus r e into u bar by h is equal to 0. So, here similarly we can write for the y component. So, u bar v bar the velocity in x and y directions s o x and s o y are the slope bed slope in x and y direction and s f x and s f y the energy slope in x and y direction r e is the excess rainfall. So, this way as far as overland flow generally overland flow we can consider as two dimension and but sometimes we can also approximate as one dimension depending upon the way we are modeling, but most certain channel flow we can consider as one dimension flow. So, these are the governing equations as far as the overland flow is concerned. So, now we have already seen say now the equations what we have seen is the dynamic wave form of this Invenance equation. So, that depending upon the condition we can say simplify into diffusion wave form or kinematic wave form. So, the diffusion wave form is shown here. So, here the continuity equation will be del q by del x plus del h by del t is equal to r e where q is the discharge per unit width and r e is the rainfall excess. So, this we can write the with respect to the diffusion wave the moment the equation will be written as del h by del x is equal to s 0 minus s f where q is equal to u bar into h u bar is the velocity in x direction and that is can be written as alpha and h to the power beta where alpha beta coefficients obtained from manning's equation beta can be written as 5 by 3 when we depending upon the which way we consider. Then kinematic wave form we can write as del q by del x the continuity equation and the moment the equation continuity equation same del q by del x plus del h by del t is equal to r e and the moment the equation is just that slope is equal to a energy slope. So, for the dynamic wave form or the diffusion wave form or the kinematic wave form now the governing equations we have seen and now to solve this equations we have to put appropriate initial and boundary conditions. So, initial conditions say if we are going for time dependent model initial conditions are required. So, initial conditions can be either we can assume the depth of flow throughout the water shadow we can assume a 0 or the discharge can be assumed a 0 and then we can apply the boundary conditions. So, boundary conditions can be we know the upstream of the water shadow like the ridge we can assume the flow depth or the flow as equal to 0 and the downstream condition we can put the gradient of del h by del x or this kind. So, gradient we can keep it as 0 or other type of boundary conditions the initially boundary conditions or the Neumann boundary conditions can be applied. So, this either dynamic wave form or diffusion wave form or the kinematic wave form as far as the overland flow is concerned we can solve this governing equations by using a numerical technique. So, you can see that to the governing equations of partial differential equations. So, we have to go for numerical solutions as far as the solution is concerned like a final difference method or final terminal method. So, we have to solve this governing equations and apply the suitable initial and boundary conditions for the considered water shadow and then we can develop the model for the say to obtain the runoff at the particular locations for the water shadow is concerned. So, here like many other losses like evapotranspiration or the infiltration all these losses we can account say as far as this rainfall access calculation is concerned. So, accordingly we can deal with the model. So, now so that is about the overland flow now coming back to the channel flow. So, the other component is the channel flow. So, this overland flow will be joining to the channel at the particular locations. So, you can see that if this is the watershed and then if this is your main channel. So, then the when the rainfall takes place the runoff will be coming from the channel overland and will be joined to the channel and then we have to route the flow through the channel depending upon the changes taking place with respect to the overland flow component. So, here the governing equations are the same same variance equation, but we can write slightly in a different way. So, the the equation of continuity is del Q by del X plus del A by del T minus Q is equal to 0. So, where Q is the discharge in the channel A is the area of flow in the channel and Q is the lateral inflow coming to the channel as overland flow and the momentum equation can be written as del Q by del T plus del by del X of Q square by A is equal to G into A into A into 0 minus SF minus G into A into del H by del X. So, this as I mentioned this momentum equation different forms we can have. So, one particular form is mentioned here. So, here this energy slope SF we can use Manning's Equational Stasis equation to get those values and then we can solve this equation simultaneously. So, that is with respect to the overland flow from various location we can route the flow and then identify what will be the discharge versus time at any particular location of the channel or the outlet of the watershed. So, that way the channel flow equations are solved. So, here also we need to go for numerical techniques like a finite difference or finite element modeling to solve these equations and then use the appropriate initial and boundary conditions. So, here also initial conditions like M depth of flow in the channel or the discharge through the channel can be initial conditions at the beginning and then the boundary conditions can be at the outlet or at the beginning of the channel what will be the flow coming or say if the channel is starting at the beginning of the watershed then there can be 0 depth. Then say now similarly similar to overland flow here also channel flow is also consents we can have the diffusion wave model and kinematic wave model. So, in diffusion wave model the governing equation is del Q by del X plus del A by del T minus Q is equal to 0 the continuity equation and the momentary equation is the simplifiers del H by del X is equal to S 0 minus S f. So, this S f we can use the Manning's equation or other J C C equation and then in kinematic approach the continuity equation is same and then we assume the energy slope is equal to bed slope. So, here also we apply the initial conditions and the boundary conditions to identify how the flow pattern is taking place how the discharge versus time or depth versus time we can identify by solving these system of equations by using numerical techniques. So, either dynamic waveform or the diffusion waveform or the kinematic waveform we have seen the governing equations and now using this governing equation using particular numerical models and we can solve the system of equations and then apply the boundary conditions initial conditions and boundary conditions and then the outputs will be the depth of flow or the discharge at any location of the channel. So, now we have seen the overland flow and the channel flow. So, if you want to say identify the there are no process taking place within the watershed then we have to couple this overland flow model and channel flow model and then we have to see the couple we have to run the coupled model by applying suitable boundary conditions for the watershed. So, this numerical modeling issues we will discuss in the next lecture and then the coupling aspect also. So, now the use of numerical simulation models. So, as I mentioned this governing equation we have to solve using numerical techniques. So, hydraulic simulation models use mathematical equations as we have seen in the previous slides to calculate the results like runoff volume or the peak flow. Then computer models allow parameters variation in space and time with the use of numerical methods. So, like final difference, final element or method of characteristics or final volume methods then the use in simulation of complex rainfall patterns and heterogeneous watershed depending upon what kind of either semi-distributed or distributed or what kind of numerical approach we use. Then evaluation of various design controls and schemes say like if there are various structures hydraulic structures how to deal with those structures and then how to deal with the various parameters variations like that. Then effective use of land use and land cover parameters. So, for the given watershed the land use land cover will be varying. So, then accordingly the say for example Manning's reference coefficient will be varying in the overland flow modeling or various parameters like porosity such as hydraulic conductivity etc. will be varying. So, that we can identify and then say the special characteristics variation if we can take care then we can have better quality or better models for the runoff model for the given rainfall conditions. So, now before crossing this lecture so, let us see some of the the classifications of the models. So, like we have seen now the modeling is based upon the Saint-Venant's equation or its variations. So, some of the examples of hydrodynamic and empirical models are listed here. So, the physical processes are listed here then the hydrodynamic models and some of the empirical models say for example, if we are dealing with surface runoff we can have the dynamic wave model or the its variations like diffusion wave model or kinematic wave model and then say a simple conceptual models like say mass balance approach models. So, various models are there some of the important models are only listed here and then empirical equations like rational methods or unit hydrograph methods or say lambo model like a CS method we can have it and then infiltration is consents we can have various forms of the infiltration empirical equations or the solution to recharge equations or renamt equation or philip two-time equations or simplified form a kinematic form. Then the empirical types infiltration models like a CS method we can also calculate based upon a CSCN or some kinds of algebraic variations or HEC models. Then groundwater variation is concerned like base flow and model based upon groundwater flow equations which we will be discussing in coming lectures and then algebraic equations like Horton equation based upon that or evapotranspressions like as we have already seen various equations we can utilize like Penman-Monday equation or Morton method or Blaney Crudel method like that. Then flow over porous bed is concerned we can either go for kinematic wave dynamic wave or volume balance models or then empirical like a CS model. Then a flow in channel is consents as we discussed kinematic diffusion or dynamic hydrodynamic models or Moskingam method or Hydrograph method analysis. Then the solute transport is concerned within the watershed model based upon advection dissipation or Fikian models we can have. So, this issues also we will discuss later or we can have some algebraic type of modeling. Then sediment transport is concerned we can go for a diffusion dynamic or kinematic or Einstein bed load based equations or sediment graph models or regression equations. So, like that if we go through the hydraulic literature large number of models we can see may be say some of the others mentioned may be thousands of models have been developed for the last few decades depending upon the conditions, depending upon the assumptions or various like 1D, 2D or 3 dimensions or the how many parameters we consider or what kind of hydraulic process are concerned. So, accordingly we can see that there are number of hydrodynamic and empirical models available in literature. So, you can choose particular model depending upon your requirement your objectives and then you can solve the particular problem as per the objectives. So, now coming back to the hydraulic models. So, you can see in literature number of hydraulic models I mean the software type software models computer models developed for specific purposes large number of models are available very few of this important models I have put here in this two slides. So, first one is so called Ilyudas model Ilyudas model Ilyudas Youllknow is Armand drainage area simulator. So, this is used for sizing of storm sewers like routines for estimating detention storage volumes. So, limitations like constant outflow from detention facility. Then PSRM models like Penn State runoff models, this is single event model and the components like overland runoff, channel routing etcetera are considered. Then HSPF model like hydrologic simulation program Fortran. So, this is either can be continuous or single event based or simulation for both quality and water quality and quantity can be considered. Then storm model like developed for original application to the San Francisco mass drainage plan. So, this is based upon conceptless view of urban drainage systems. And then we can have SWM model storm water management model. There are routines for surface, subsurface or ground water components and this can be fully dynamic hydraulic floor routing. Then we can have HEC series or HEC HMS models. So, it can be either doors based or windows based. Then these models can be used to calculate runoff hydrograph at each component like channels, then various locations etcetera. Then WMS water shed modeling system. So, this provide the link to various available model using the GIS package and hydrologic models. So, including like HEC, TR 55, TR 20 there are link to links to this various model in the water shed modeling systems. And then I HECRAS. So, this is a particular model simulation of stream flow from basins of various sizes unit hydrograph approach to lumbered modeling. So, if you go through the hydrologic literature you can see number of models like this. So, as I mentioned depending upon the requirement, depending upon the objectives you can choose this particular model or you can develop your own model also depending upon your requirement. So, now finally, what are the important steps in water shed simulation analysis when we are going for water shed simulation and the steps include. So, first we have we can choose the model depending upon the your the objectives or the requirement and that availability. And then we have to collect the data input data collection like rainfall, infiltration, physiography, land use, channel characteristics etcetera. Then we can evaluate the study objectives under various water shed simulation conditions. So, we can see various scenarios and then accordingly we can simulate. Then selection of methods for obtaining base in hydrographs and channel routing as far as hydrology is concerned for the given rainfall condition or the given intensity of rainfall the possible rainfall how the system will be behaving. Then we can we have to do calibration verification of the models as we discussed earlier. Then model simulation for various conditions say for example, if a dam is built of this particular height what will happen how much is the storage possible. So, like that various conditions we can simulate and then various parameters sensitivity also we can carry out. Then we can evaluate the usefulness of model and then come and on the newer changes as far as the water shed modeling is concerned. So, these are some of the important steps in water shed simulation analysis. So, now before closing this lecture. So, here two examples one is distributed model based upon a kinematic wave approach. So, here the kinematic variations we have already seen. So, here the we consider an area of 400 this is for overland flow 400 meter by 500 meter size area and slope S0 is given as 0.0005 minus coefficient is 0.02 and we apply uniform excess rainfall R is equal to 0.33 mm per minute and duration is 200 minutes. So, this is the area we consider. So, we have to identify how much is the runoff taking place with respect to time for this overland area. So, for this actually Jaybar and Mokhtar in their paper in 2003 given in say they are given the analytical solutions. So, the solution is given by this equation. So, I am not going the details of this equation. So, this Q0 percent the discharge or ploper unit width. So, then alpha and beta some of the coefficient and then here T is the Tz is the time of concentration T as the rainfall duration Tf is the simulation time and this also we have done this the overland flow simulation by using a finite element model which we will be discussing the next lecture. So, we run the model and then we simulated by using the kinematic wave approach and then it is corresponding analytical solution also you can see here with respect to time how the discharge variation is given here. So, this line represent the analytical solution and then the kinematic wave model results for two time step one is 30 second and another one is 180 seconds. We can see that there is a good match for the analytical solution of the kinematic wave model, but you can see that this analytical solution we can apply only for very simple cases like this, but for a field case we cannot how these kinds of analytical solution, but since we developed a model based upon finite element method for the solution of the kinematic wave approach. So, we used this analytical solution for verification of the developed model. So, the corresponding finite element formulation will be discussing the next lecture and then another application to a case study area called Benakha water shed as I mentioned in civil department IIT Bombay we have developed some water shed models based upon the kinematic wave approach and diffusion wave approach using the finite element method. So, that models we have applied for water shed called Benakha water shed. So, the modeling details we will discuss in the next lecture, but here my purpose is to discuss the variation the physically based model application and to identify how the runoff is taking place for the given rainfall condition. So, here the water shed is located in Chattra district in Charkhand stage and area is 16.7 to square kilometer, major soil class is sandy loam and here we use remote sensing data and GIS is used for drainage slope and LULC maps. Then mining surface all these details we obtain from using the GIS and so mean value of slope and mining surface for each grid is a sense and then accordingly the variation is taken. So, this is the water shed and this is the main channel this is the outlet of the channel. So, this shows actually we developed a digital elevation model for this water shed and this is showing the elevation variation for the water shed. So, here this is the variation with respect to the water shed and then here this shows the slope variation and then this shows the land use variation for the water shed. So, this is the grid which we utilized using the final term method. So, this is a one dimensional modeling approach. So, these are different strips which is joining the outlet of the channel. So, this is the main channel for the water shed. So, here we used a diffusion wave approach for the overland flow and channel flow modeling and then a field model is used for the infiltration. So, here we did not be we considered only the say even based models. So, that way evapotranspiration effects were not considered only the infiltration effect was considered. So, as we discussed we have done number of calibrations and then validations and for especially for infiltration models various parameters like saturated hydraulic conductivity, initial soil saturation, porous distribution, pore size distribution, effective porosity all this identified for the given data sets and then we calibrated the model and we obtained this parameters and then validation and calibration details are shown here say for example particular event of July 24, 1996 this is the rainfall pattern and at the outlet of the water shed we have simulated the runoff discharge versus time and then we compared with some of the observed data for calibration and then this is for validation events. So, even though there is some variation with respect to observed and simulated, but in physically based model these kinds of variations we expect since we are not able to capture the entire variation of the data like input data especially the infiltration data is very very difficult to obtain. So, that way some of the parameters we started with the literature values and then we tried to calibrate and those parameters were used for the modeling. So, now these are some of the important references which were used in today's lecture. So, like this paper which you published in the hydrologic process. So, this is the case studies based upon this paper. Then say some of the tutorial assignment and self-evaluation questions. So, tutorial question is illustrate the various hydrologic process from rainfall to runoff in water shed based modeling for a typical water shed assess the important hydrological processes and discuss various models available to analyze these processes describe the merits and demerits of each models for a selected water shed how to find the runoff for a given rainfall even illustrate with examples. So, these details these are based upon today's lecture. So, you can easily get the solution. Then say self-evaluation questions describe different categories of deterministic hydrologic models. What is the importance of physically based water shed modeling? Then describe the Saint-Venan's equation with its applications, assumptions and importance. Come by the following lumbered semi-distributed and distributed models HEC HMS SWMM Ike 11 models discuss the applications advantages disadvantages of each model. Then a few assignment questions differentiate between lumbered semi-distributed and distributed models used in hydrologic modeling. Then how physically based water shed modeling is done illustrate the step by step procedure what are the advantages and limitations. What are the important steps in the water shed simulation analysis illustrate various types of hydrodynamic and empirical models used in hydrology. So, all these questions you can answer based upon today's lecture. Finally, one unsolved problem for your water shed area discuss the possibility of applying a physically based model for a runoff or flood analysis. Identify the data required for physical modeling develop a conceptual model by giving the detailed steps for rainfall runoff modeling. Then identify how to model evapotranspiration, interception, infiltration for the area considered. With respect to available data choose specific models to model these processes and discuss how to add this process in the rainfall runoff modeling. So, based upon today's lecture and the previous lectures you can easily do this say unsolved problem. So, now today we discussed the hydrologic modeling based upon the physically based approach. Now, in the next lecture we will discuss some of the numerical tools how to solve these ends of Saint-Vinand's equations or its variations and then we will discuss some more case studies. Thank you.