 Namaste and welcome to the video course on watershed management. In module number 4, lecture number 15, today we will discuss about the watershed modeling approaches. So, some of the important topics covered today includes the standard modeling approaches, system concepts, classifications, black box model, lambda model, distributed model, rainfall runoff modeling and some of the important keywords for today's lecture includes watershed modeling, system concepts, black box model, lambda model and a distributed model. So, as we discussed earlier, when we are going for watershed planning and management, so we have to see the response of various resources in that system say one of the most important resources the water within the watershed. So, the watershed water is concerned as a resource water main source is from the rainfall. So, that means, the for the given precipitation conditions we have to identify how much will be the runoff. So, runoff condition we have to simulate. So, especially say in this context, so we have to do modeling of the watershed. So, in a watershed model means in watershed models we simulate the natural processes of the flow of water, sediments, chemicals, nutrients and microbial organisms and quantify the impact of human activities on these processes. So, that means, say in a watershed, so say when we interfere in terms of various land use and various other activities then there will be lot of changes will take place. So, we can identify what will be correspondingly to the particular changes what will be happening to various processes. So, that way the watershed model simulates the natural process of the flow of water it can be water or sediments or chemicals or nutrients like that. So, for the say given type of activities or for the particular activities say how it is going to affect these processes. So, that is what we are going to simulate by using the watershed model. So, in all this we can see that the simulation is for this the processes place as far as simulation is concerned simulation of this processes place and a fundamental role in addressing a range of watershed based water resource, environmental, social and economic problems. So, when we are developing a particular watershed plan or a watershed management program. So, we have to see when we are interfering within the system say for example, when we are going to construct a check dam then how much water can be stored what will be the how the system will be behaving. So, all those things we have to identify. So, we may be simulating say for various problems like water related problems or environment related problems or social and economic related problems. So, that way the watershed models are very useful actually watershed models are essential while developing the watershed management plans. So, as far as watershed model is concerned as I mentioned this is one of the important say tool to see that how the system is responding. So, that way we can say that watershed model is a tool which addresses a wide spectrum of environmental and water resources problems for the given watershed or for the given river basin or catchments which we consider. So, the when I say the wide spectrum number of problems we can address through this watershed say various type of watershed models. So, the spectrum of problems that we can handle with watershed models include water resource planning, developments, design, operation and management. So, that means, if you are going to develop a reservoir within the watershed then how to plan it and how to develop it and then we can see how to manage it. Then we can also simulate like the flooding problems then drought problems then like erosion problems like a soil erosion, sedimentation then stream bank erosion, coastal erosion, sedimentation, non-bond source of pollution, water pollution from industrial, domestic, agricultural and energy industry sources, migration of microbes, deterioration of lakes, desertification of lands then degradation of lands, decay of rivers, irrigation of agricultural lands, conjunctive use of surface and ground water, reliable design of hydrold structures and river training, works etcetera. So, as I mentioned we can develop watershed models for a wide spectrum of problems so that we can easily understand what will be the effect of various interventions within the watershed and what is going to happen within the watershed say like if you are going to construct a check dam say what will be the as far as water management is concerned how the system is going to behave or when we go for say the soil conservation measures how the soil erosion can be reduced or when we are going for say the environmental planning like reduction of the pollution sources then how the system is going to behave. So, all these aspects we can address by simulating the particular type of watershed model. So, now when we are discussing about the watershed model say generally we can go for a system approach. So, say as we have already seen we will be considering the watershed as an area or as a particular domain so that particular area we can consider as a system and then within that system say what will be happening. So, most of the time we will be looking to the watershed simulation using a model by using a system approach. So, in the system approach say for example, if you say water related problems are concerned we can use various conservation principle like conservation of mass, conservation of momentum, conservation of energy etcetera. So, if you consider conservation of mass then we can see that inflow minus outflow is equal to rate of change of storage. So, like that we can develop particular system of equation for the given watershed area by using a system approach. So, system approach we can generally we use for watershed modelling. So, system approach the problems involves in three steps. First one is we can we have to describe the system. So, describe the system means say we identify the boundaries of the system and then various other features within the system. So, this involves modelling the watershed system. So, we can identify the domain then boundary conditions and other parameters as far as the system is concerned. And then a second problem can be describe the objective function say generally in the system say whatever we are going to say the water say resource. So, whether we may be going for optimization so like minimize the cost and maximize the benefits so like that. So, that way we can describe an objective function say generally stated in terms of economic terms like minimize the flood hazards or maximize the water availability so like that. So, second problem can be we can describe the an objective function and in terms of that then within by using say certain constraints so we can optimize the total system. So, the third problem can be optimization of the system. So, in systematic approach or system approach say we describe the system and then we can go for a simulation of the system then we can go for optimization of the system. So, as far as various watershed model models are concerned so most of the time we are looking for a design problems say as far as what is happening with respect to the particular resource like water is concerned so we will be looking to the design problems. So, this design problems we can classify into three categories first one is long run type of problems. So, long term long run means so we look into say once a system is developed say we will be looking to what is happening for a long time like say one year two years or a number of years what will be the system. So, in long run say for example design of multipurpose resource system so huge capital investment will be there. So, we have to see the benefits after say over a long period of time so what will be the how the system will be behaving. Then second say classification is intermediator run. So, intermediator run say for a short period like maybe it can be for few months or it can be for few weeks like that. So, like say for example irrigation cultivation for a particular season so for we know how much is the storage within the reservoir and then how we can plan as far as the water release is concerned. So, that is as far as the intermediate run is concerned and then a short run design problems means say it is say for a for a day or a few days or few hours say how we are going to manage the system. So, say for example how much water to be released for flood control. So, the rainfall is taking place continuously so then we have to release the water from a reservoir. So, to control the floods so how to operate the system so that is say a short run problem. So, in all these either long run or intermediate or short run so we may require hydrologic modeling and then we may have to identify various situations and then we have to go for alternate models. So, it is always say there will not be a unique solution number of solutions will be there and each solution will have its own advantages and disadvantages. So, we have to identify we have to study each of this scenarios or situations using different types of models and then we have to say choose particular models. So, then as far as water shed models are concerned so we have to choose or we have to say select particular model using certain criteria. So, depending upon what are our objectives, what are the resources to do the simulation or the modeling then so also it depends upon the accuracy. So, how much accurate should be the results what we are getting so then we are always looking for in say a complex natural system by using number of assumptions we are simplifying the system. So, the simplicity of the model or modeling approach we have to see and then some aspect like consistency and sensitivity so with respect to various parameters so all these aspects we have to consider when we look for particular water shed model or particular modeling approach by using a system approach. So, now we have seen say most of the time we are using a system approach as far as the water shed modeling is concerned. So, most of the time say for example, if water resource is concerned we have to see the various hydrologic processes taking place from precipitation to runoff as we discussed in the previous lectures like various losses like interception evaporation infiltration etcetera will be there. So, we have to consider all those aspects while going for a rainfall to runoff modeling. So, then say for the last few decades a number of models have been developed by various researchers by considering various theories and various aspects and say by using number of assumptions also there are very simple models to very complicated models. So, accordingly we can broadly classify the available water shed models into three types. So, the types are black box models, lumbered models and distributed models. So, as far as a water shed model when we say a black box model. So, these models describe mathematically the relation between variables say for example, rainfall and surface runoff. So, without describing the physical process by which they are related. So, when we are say we are using a black box model that means say for example, bottom diameters are rainfall and runoff. Actually as we discussed earlier number of processes will be there physical process will be taking place from rainfall to runoff. But in black box models we are not considering all these physical process what is taking place within the water shed. But we are looking say we are developing simple relationship between the rainfall and runoff which may be particularly suitable for particular location or particular water shed depending upon the various parameters. So, actually this black box models are very simple models very easy to use, but then it may not be universally applicable and then it has got its own limitations since most of the physical process are not considered as far as this model is concerned, black box model is concerned. So, some of the example include like unit hydrograph approach then artificial neural network for a particular say rainfall to runoff modeling for a particular location then rational formula etcetera. So, these are all say simplified forms which is simply give a relationship between say rainfall to runoff and then say for example, in artificial neural network say by collecting the data for a long duration may be for many years say how the runoff is taking place at a particular location or at outlet of water shed then we can say if you know the rainfall and runoff. We can identify say a relationship for that particular location valid for that particular location by considering the available rainfall and the runoff. So, that way so this that then it is called as simply a black box model since we do not consider most of the important processes taking place within the water shed what is happening. And then a second type of model is called a Lambodou models. So, Lambodou models occupy an intermediate position between the distributed model and black box models. So, here you can see that say some of the aspect of the physical process are taken here, but not all the important aspects of the physical system, but some system like concentration of mass is considered say while considering the when we are saying that symbol model like inflow minus outflow is equal to change in storage. So, that is actually we are concerned the consideration of mass principle. So, that that kind of model is a Lambodou model. So, but it is that kind of model say we will not consider all the physical processes taking place within the water shed. So, say for example, our soil conservation cover number method which we will be discussing in today's lecture. So, that is a Lambodou model and then Stanford water shed model is a Lambodou model and then this mass balance type models are all Lambodou models. And then the next type of model is called distributed models. So, these distributed models a number of different types of models are available. So, in the distributed models we consider all the physical processes taking place within the water shed say for example, if we consider rainfall to runoff. So, then we will be solving the governing equations say for example, partial differential equations such as Saint-Vinand's equations or Navier-Stokes equations which you consider consideration of mass then consideration of momentum. So, most of the important physical processes taking place the water shed or we consider in that and then we develop a model. So, like when we solve the Saint-Vinand's equation for overland flow or channel flow using a numerical tool like a final difference method or final terminal method. So, that kind of model is called a distributed model. So, here the distributed model consideration of a distributed model is very complex we need a large number of parameters and then so much of efforts are required. But the advantage is that that type of distributed model gives all the processes taking place. So, it shows the physics of the problem so that way that has say when we consider the total processes taking place in the water shed that is very important say this distributed models are very important as far as the water shed modeling is concerned. So, that way now as we have seen so we can classify the water shed models into black box model then lambda models and the distributed models. So, as we already seen earlier the say when we develop a water shed model so the structure of the water shed model we can see. So, what we are trying to see is the simulation of process that takes place within the water shed. So, most of the time the aim is to gain better understanding of hydrologic phenomena operating in a water shed and how changes in water shed may affect this phenomena. So, as I mentioned if say for a given rainfall condition how the runoff will be taking place or say once we adopt various measures say for example, for soil conservation measures or in water harvesting measures so what will be its impact so that is what we are trying to understand through a simulation models. So, as we discussed earlier any of the water shed models there are mainly three steps. So, we have to formulate particular water shed model so first we have to conceptualize the model and then there may be say if you are going for physical modeling then the particular governing equations we have to consider boundary conditions we have to consider and then we may develop the model or we can get the model from outside sources so that is the first step that is the formulation. Then we have to calibrate and verify that particular model so the calibration processing load identifying various parameters which governs the various processes taking place within the water shed and then verification means we are trying to identify say whether we are checking whether the model is given the appropriate results so that is verification and then we apply the model for particular simulation for the given condition so that is the theorem is the application. So, generally as we discussed earlier also any of the water shed model constitute there will be an input function and then there will be an output function and then there will be transform function. So, as you can see that the input function can be the rainfall taking place within the water shed then output function can be the runoff taking place within the water shed and transform function is various processes taking place between the rainfall to runoff like interception losses infiltration losses and various losses taking place within the water shed when this transformation from rainfall to runoff takes place. So, that way we will be modeling a water shed. So, now say we will be discussing various types of hydrologic models so we can see that in literature say considering the types of model which are developed or various methodologies adopted or what kind of phenomena or model. So, accordingly we can see different types of models. So, now we will discuss the hydrologic models. So, first classification is the hydrologic model can be either event wise or continuous wise. So, event versus continuous models. So, event model means it represents the model represents a single runoff event occurring over a period of time ranging from about an hour to several days. So, this event modeling is very important say when we are looking for the flood simulation of a water shed. So, since flooding most of time taking place say for a heavy rainfall for few hours and then with respect to that how much is the runoff is coming and then accordingly we may have to identify how is the process taking place. So, we have to identify event wise say we know the say it minute wise or at least hour wise we have to identify say the rainfall process and then the runoff process. So, by considering all the hydrological process taking place. So, we need a lot of data. So, the accuracy of the model input output depends upon the reliability of initial condition. So, event model can be say like a flood simulation model for a water shed or an urban water shed. Then second variety of here is continuous models. So, continuous water shed model will determine flow rates and conditions during both runoff periods and periods of no surface runoff. So, this is for a long time simulation. So, it is not simply the during the event, but after the events also. So, what will be happening? So, maybe it can be for weeks or for months or maybe for a year. So, like that or few years we are simulating the various processes continuously. So, we may have to give the initial conditions and then we utilize the runoff components like direct to a surface runoff, then shallow surface flows, indoor flow and ground water flow. All these components we may have to consider in the continuous water shed simulation. So, here say for example, when we are developing a dam or a check dam at the outlet of water shed, we may have to do a continuous simulation, continuous water shed model. So, that we can identify say once the rainfall is taking place then water is stored and then for how many months or how many say season we can utilize that water. So, there we have to consider various losses also. So, an event model may omit one or both of the subsurface components and also evapotranspiration depending upon the modeling accuracy we are looking for. So, but continuous water shed model we have to consider the evapotranspiration losses and also the various subsurface components. So, that is about the event versus continuous models. Then second type of model is called complete versus partial models. So, complete models or comprehensive water shed models. So, here we consider most of the hydrologic processes taking place. So, this here we source the water balance equation then it represents more or less all hydrologic processes. Then say it increases the accuracy of the model since all the aspects are considered in the simulation process. Say for example, say rainfall to run out at the particular location of the water shed outlet say we want to identify how is the flow pattern taking place. So, that way a comprehensive or complete water shed model consider most of the important hydrologic process. Then partial models means it represents only a part of the overall runoff process. So, we may not consider say for example evapotranspiration or infiltration or various other processes. So, for example, water yield models gives runoff volumes, but no peak discharges. So, it will not give a holistic picture of what is happening if we use a partial model. Then another classification is with respect to the calibrated or calibrated parameter versus measured parameter models. So, calibrated parameter model means one or more parameters that can be evaluated only by fitting computed hydrographs to the observed hydrograph. So, here say we can calibrate various parameters based upon the observed and we will try to fit with the computed hydrographs. So, this is necessary if the water shed components has only conceptual component models. So, the period of record flow is needed for estimating the parameter values. And the second category here is measured parameter model. So, here we are trying to determine the parameters from non-water shed characteristics. So, the water shed characteristics are already known. From that we can identify the parameters. So, area and channel length like this type of parameters maps and channel cross section measured in the field. So, these are all non-parameter. So, usually we use these kinds of models to totally for engage water shed. So, the bottom measured parameters we directly put, but some of the other parameters which are difficult to measure we use the standard values. So, then another classification is say as far as models are concerned as we discussed earlier also. So, this is two important types of model modeling concept which we use in hydrologic modeling. So, that is lumbered versus distributed models. So, as we discussed so lumbered models means if we implicitly take into account the special variability of inputs, outputs or parameters. So, we lump the system for the given water shed or given zone of the water shed since we do not know the exact behavior in a distributed way. So, then we utilize the average values of the water shed characteristics affecting the runoff. So, this may lead to significant error due to non-linearity and threshold values. So, as we have seen earlier say water shed is concerned various parameters are changing from one location to another location. So, what we do we consider for a either for the total water shed or for the particular zones we consider for the water shed we lump various parameter by taking an average value and then we run the model. So, that is called a lumbered model and second category here is called a distributed model. So, distributed model include special variation in inputs, outputs and parameters. So, here most of the bottom characteristics of the water shed are considered and then we look say how the variation is taking place. So, division of water shed area into number of elements and calculation of runoff volumes for each element. So, anyway in any kind of model we cannot represent all the aspects as far as the variations are concerned. So, a totally distributed model by considering all the variations of various parameters are an impossible task in water shed modeling. So, what we do we can consider small small zones or small small elements or grid and then we can average various parameters like manning's reference coefficient or the hydraulic conductivity or porosity or like that various parameters and then we consider as much as possible that these parameters variations. So, when we consider modeling like that that type of models are called a distributed models. So, then now finally, we have seen the various classifications as far as the models are concerned. So, again say by considering what we are discussed so far. So, as far as hydrologic models are concerned now hydrologic models are also part of water shed models. So, hydrologic models mainly deal with the rainfall to runoff process. So, that way hydrologic models we can classify into two categories. One is deterministic type of hydrologic models and second one is stochastic hydrologic models. So, deterministic hydrologic models means it is deterministic. So, many of the parameters are deterministic. So, we are not considering any probability or the stochasticity as far as the system is concerned. So, here we use typical type of equations or we solved typical type of governing equations in a deterministic way the various parameters we assume are known and then we are trying to find say for example, rainfall to runoff or various hydrologic processes are concerned. Then the stochastic models we consider the stochasticity or the probabilities condition say like the rainfall is a probable parameter. So, its variation we consider with respect to probabilistic distribution or stochasticity. Then like various water shed parameters like hydrologic conductivity or the parameters which drastically varies, we consider its probability distribution and then how it is varying. So, that way when we model that kind of hydrologic models are called stochastic hydrologic models. So, as far as deterministic hydrologic models are concerned, we can again classify like empirical models. So, there we are using typical type of equations. So, just like a rational formula or some of the black box models. So, that is so called empirical model. Then we are having the Lumbered models. So, Lumbered models means say some of the aspects like say consideration of mass or that kind of system is considered. So, that is so called Lumbered model. So, SCS curve number method is a Lumbered model and semi-distributed model. So, semi-distributed model means all the variations are not considered or it is not fully distributed model. Some aspects we lump with respect to various parameters, but some aspects we consider the distributed. So, then we call it as a semi-distributed model. So, then other type of model is the last one is so called distributed model. So, various parameters, distribution we consider and then we consider the real physics of the problem. We solve the governing equations, partial differential equations which governs the hydrologic process and that type of models are called a distributed models. So, now when we discuss hydrologic modeling. So, in the last few lectures we have discussed the various hydrologic parameters which governs say for example, rainfall to runoff. So, this we have already seen. So, when we consider the hydrologic modeling, so say for example, for the given rainfall condition how much is the runoff or at the outlet of a watershed, how is the flow pattern will be varying. So, then we have to consider the various hydrologic processes taking place within the watershed. So, this we start with the precipitation or the rainfall. So, then as we have seen various losses like interception and then the depression storages that we have to consider. Then like evapotranspiration will be taking place. So, that we have to consider. Then say there may be some surface storage as far as the area is concerned. Then once the surface storage has full the runoff starts. So, the surface runoff so called overland flow. Then infiltration also simultaneously is taking place from the watershed. So, that infiltration will be going to the soil and then it may reach to the aquifer system. So, then there can be also coming back flow called interflow. So, in all these there will be vaportranspiration and finally all these interflow coming together with surface runoff is called direct runoff and that will be joining the channel. So, that is called channel flow and its corresponding processes. Then with respect to infiltration and then groundwater flow condition there will be interaction between the groundwater and the surface water. So, that is the groundwater base flow taking place. So, that will be joining the channel flow and of course, reverse also. So, this shows a typical hydrologic modeling from precipitation to runoff say by considering a particular watershed. So, depending upon the type of model which we can develop. So, we may consider some of the important say processes in this like of course, precipitation and runoff we have to consider. But now like interception we may not consider or say the interflow component we may not consider. But of course, infiltration is one of the important parameter which we have to consider and then evapotranspiration also. So, that way the hydrologic model we can develop say it can be either simplified model or complex model or a semi complex model depending upon and the what type of hydrologic processes will be considered as far as the model which we develop. Now say when we are going to select a particular watershed model. So, we have to see certain criteria we are meeting. So, what are the important criteria? So, the important criteria I have listed here. So, we may have to look into various assumptions which we are using. So, first we delineate the watershed and then we are looking whether of course, the flow say for example, the when we are going for flow simulation, flow is taking place in three dimension, but we may consider as the flow variation as two dimension or one dimension. So, that kind of assumptions we can put and then we can conceptualize a model. So, that is assumptions and conceptualization step. And then the ability of model to predict variables required by the project or required by the objectives. So, already if we know the objectives what we are trying to do. So, according to the objectives the selected model or the model which we are going to choose. So, whether that will have the ability to give those particular values or particular results. So, that is the ability of model to predict the variables. Then hydrologic processes that need to be modeled to estimate the desired output adequately. So, like a single event model or continuous process. So, that is another selection criteria. Then of course, most important aspect is whether we have sufficient input data. So, if sufficient and accurate input data is there then only we can go for very complex models which can give better results. But if sufficient data by considering various aspects are not there then we have to go for simplified models. And then of course, we have to see a good modeler is available like a expert is available. And then if you are going for computation model then computation facility we have to see. And then what is the cost which we can pay for that particular say modeling. So, like what is the price of if you are going to choose a software or if you are going to hire an expert then what is the price which we may have to pay. So, these are some of the important selection criteria as far as when we look for a watershed model in the case of watershed simulation considered. So, now here I have listed some of the important steps which we say systematically follow as far as watershed simulation or analysis is concerned by using models. So, first one is once the watershed is conceptualized and then various aspects we know and then our objectives are set then we can go for particular model. So, first step is we select the model or selection of model. So, this depends upon the various assumptions what kind of what type of objectives we are setting. Then next step is input data collection. So, data collection like rainfall, infiltration, physiography, land use, channel characteristics etcetera we have to get the input data. Then evaluate the study objectives under various watershed simulation conditions. Then a selection of methods for applying say like a base in hydrographs and a channel routing. So, this is what kind of methodology we are choosing. Then calibration and verification of the model then we go for model simulation for various conditions. Then as we discussed earlier we may have to go for sensitivity analysis of various parameters. Then we may have to evaluate the usefulness of model and then we may have to do we may have to comment on various aspects as far as the simulation is concerned. So, these are some of the important steps which we consider as far as the watershed models are concerned. So, now in the next few slides we will concentrate upon the rainfall runoff models which we commonly use. So, first we will discuss some of the black box models or some of the empirical equations and then we will discuss a lumbered model. So, called soil conservation service cover number model. So, now we will discuss the surface runoff estimation. So, some of the important empirical equation one of the most commonly used empirical equation is so called the rational methods. So, by using the rational method this is a relationship given the discharge or flow area versus the rainfall for a given rainfall intensity. So, Q is equal to C into I into A where Q is the in the discharge or the flow C is the so called runoff coefficient I is the rainfall intensity and A is the area of the watershed which we consider. So, this we can write as small Q is equal to 0.0028 C I A where small Q is the descent peak runoff rate in meter cube per seconds and C is the runoff coefficient and I is their rainfall intensity in millimeter per hour for design return period and for duration equal to time of concentration of the watershed. So, this time of concentration is the maximum time which you may take from take for the water particular from the farthest point of the watershed. So, this we will be discussing in the coming slides. So, and A is the watershed area in hectares. So, C is the runoff coefficient as I mentioned which shows the rate of peak runoff rate to rainfall intensity. So, these are dimensional parameter, dimensionless parameter. So, C varies as per slope, land use etc. So, say for example, values can vary from 0.3 to 0.6 say if the slope is varying from 0 to 5 percent then 0.1 to 0.3. So, like that that depends upon the land use of the particular watershed area. So, for a given watershed, so if the land use is varying from one location to another location. So, we can put a different zones say like area can be given to A1, A2, A3 etc. Then for each land use we can identify the runoff coefficient and then for the total watershed we can identify the average runoff coefficient which is C is equal to C1, A1 plus C2, A2 plus C3, A3. So, for example, three land use and three areas. So, then divide by total area A is equal to A1 plus A2, A3. So, that way we can use this rational method for the given watershed. So, you can see that here the various watershed this watershed is concerned the land use is changing. So, that way we can make an average runoff coefficient. So, here this is one simple formula which we can which is very commonly used and then it is based upon number of assumptions. So, it is not an accurate method to get the runoff for a given rainfall condition, but it is an average method which shows a tendency of the flow condition. So, this rational method is based upon number of assumptions like rainfall occurs at uniform intensity and with TC equal to the time of concentration of watershed. Then second assumption is rainfall occurs at the uniform intensity over the whole area. Then maximum runoff is directly proportional to rainfall intensity. Then peak discharge probability is same as rainfall probability. Then runoff coefficient does not change with a storm type. So, these are some of the important assumptions which we utilize in the this rational method. And then so as I mentioned this time of concentration is very important say in this method. So, time of concentration is the time needed for water to flow from the most hydrological distance point in the watershed to the outlet once the soil has become saturated and minor depressions are filled. For example, if this is our watershed and this is the farthest point of the watershed. So, this is the outlet how much is the time taken for the water to flow from the distance point to the outlet. So, when duration of rainfall storm equals time of concentration all parts of the watershed contribute simultaneously to the runoff at the outlet. So, once that time of concentration is reached from all parts to the outlet the runoff will be taking place. So, here this figure shows the time of concentration say here this is the time of concentration. So, this is the hydrograph time versus the runoff. So, this time of concentration is one of the important parameter which we have to consider. And this rational method is one simplified method. So, which give an overall range. And as far as time of concentration is we have to identify. So, number of equations are available based upon various observations by various researchers. One of the commonly used equation is so called Kripitz formula which was proposed in 1914. So, that is T c time of concentration is equal to 0.0195 L to the power 0.77 into S g to the power minus 0.385 where T c in minutes the time of concentration minutes L is the maximum length of flow in meter, S g is the watershed gradient in meter per meter. So, this is the difference between outlet and most remote point divided by length L. So, this is generally used to identify what will be the time of concentration. And now nowadays we can also use a modified Kripitz equation that is given by T c is equal to 0.01195 L to the power 0.77 S g to the power minus 0.385 plus 2L 0 N divided by square root of S 0 to the power minus 0.467. So, where say L 0 is the length of overland flow in meter, S 0 is slope along path in meter by meter, N is the manning's roughness coefficient. So, here you can see how this T c is considered. So, say N is we have we can identify from the literature like for poor grass cultivated rock crops N is equal to 0.2 and smooth impervious we can write N is equal to 0.02 like that. So, we can identify for the given watershed conditions what will be the time of concentration and then we can use this the rational method to get the design peak runoff for the given condition. So, generally this rational method even though it is used for a larger radius but it is generally it is limited to area less than 800 hectares, but some of the practitioners use for larger area also. And then some other empirical equations are available based upon real field observations actually that type of equations are valid only for that particular locations particular situations. So, here I have listed some of the equations which are commonly used in the Indian conditions. So, first one is so called Dickens formula. So, here peak rate of surface runoff in meter cube per second is equal to C into 8 to the power 0.75, A is the area in square kilometer, C is the coefficient. So, this can vary from 11.45 for annual rainfall of 610 to 121,270 mm. And then another commonly used equation is called Rives formula that is also very similar to Dickens formula, Q is equal to C into 8 to the power 0.67. So, same Q A and C, but here C varies from 6.76 to 40.5 depending upon location of watershed. And this is generally developed for South India. So, this type of equations are based on practical experience and long time observations, but this we cannot apply anywhere, but wherever it is developed by considering the rainfall, considering the runoff conditions, these equations are developed and for that particular area we can utilize it. And then another equation is so called Emmerich equation is called Cook's methods. So, this method is based upon relief, soil infiltration, vegetation, cover and surface storage. The equation is Q is equal to P into R into F into S. So, here approximate weightage are aligned for these parameters. So, where Q is the peak runoff for specific region, P is the peak runoff from groups, then R is the geographic rainfall factor from groups, then F is the return period from groups, S is the shape factor from a table. So, here this shows the area versus peak runoff variations. So, these are empirical equations are developed based upon the observation for a particular area. Then there is so called soil conservation service method. So, here also this is evolved for uniform rainfall using assumptions for a triangular hydrograph like this. So, assumptions of rational method and corresponding SES triangular hydrograph is valid here also. So, here Tp the time of peak is given by d by 2 plus Tl that means equal to d by 2 plus 0.6 Tc. So, d is the duration of excess rainfall, Tl is the time of lag and Tc is the time of concentration, Tc is equal to Tl by 0.6. And then Tc also can be approximated using this equation. So, here L is the longest flow length in meter, N is the runoff curve number and Sg is the average watershed gradient. So, this is so called soil conservation service method. And then the peak flow rate we can identify q is equal to q N into A into q where q N is the unit peak flow rate. Then A is the watershed area and hectares and capital q is the runoff depth in millimeter from curve number methods. And then unit peak flow rates are developed for a particular region using the time of concentration and ratio of initial abstraction to 24 hour rainfall. So, that is so called SCS methods. Now, another important method which is a lumped model is so called SCS soil conservation service curve number method. This method is very commonly used in many countries and it is one of the accurate method used for identification how much is the runoff is possible for the given rainfall condition. So, SCS curve number method is developed based on observation in agriculture watershed in America for a long time rainfall and runoff by United States Department of Agriculture in number of watersheds in USA for a long period say in 1940s and 50s. So, SCS curve number or soil conservation service curve number method nowadays called as NRCS curve number method natural source conservation service method. So, this is based upon recharge capacity of a watershed and recharge capacity is based on andeserant moisture content and physical characteristics of the watershed. The curve number is an index that represent the combination of a hydrologic soil group and andeserant moisture conditions. So, we say as per the SCSC and various hydrological soil groups have been classified into four categories group A, group B, group C and group D. So, group A it is the soil type is a lower runoff potential. So, soil with high infiltration rates when thoroughly wetted consisting mainly of deep well to excessively drained sands and gravels high rate of transmission and group B is moderately lower runoff potential. So, here moderate infiltration rates moderate rate of water transmission and group C is moderately high runoff potential and a slow infiltration rate and group D is high runoff potential and slow infiltration rate like a clay pan or clay layer. So, these are generally used for soil groups and then this also method is based upon andeserant moisture conditions so called AMC condition which is an index of watershed wetness which is determined by total say by considering total runoff in five days period preceding a storm. So, there are three conditions AMC one which shows the lowest runoff potential. So, soil is dry enough for cultivation then AMC two means average condition and AMC three means highest runoff potential. So, practically the soil is saturated so that immediately the runoff starts. So, then in this method the potential maximum retention storage of watershed is related to curve number which is a dimensionless number varies from 0 to 100. And if I a is the initial amount of abstraction like interception, depression, storage and infiltration then it is assumed that the ratio of direct runoff q and rainfall p minus initial loss p minus I a is equal to ratio of actual retention to storage capacity. So, we can write q by p minus I a is equal to p minus q minus I a divided by s. So, where I a is the initial amount of abstraction. So, generally I a is assumed to be a fraction of this storage s and generally taken as I a is equal to 0.2 s. So, now from this equation number one we can write the q which is we have want to identify q is the runoff direct runoff. So, that q is equal to p minus 0.2 s all square divided by p plus 0.8 s. So, knowing here in this equation it is a one parameter model. So, knowing p and s the rainfall and the s that means the storage then we can get the runoff. So, q as same unit as p in millimeter. So, for convenience we can generate a number called curve number. So, c n is equal to 25400 divided by 254 plus s where s is the richer capacity of watershed. So, we identify curve number based upon this and that is varying from 0 to 100. So, for the given hydrologic groups of soils and then andesite moisture conditions s e s curve number manual gives the various curve numbers for various land use or land cover and treatment type of practice then hydrologic conditions. So, various numbers varying from 0 to 100 are assigned. So, you can see this table. So, these tables are given in most of the hydrologic test book. So, above table give for a andesite rainfall condition 2 and average condition. So, various tables available for various conditions we can obtain from based upon that and these are available in standard test book. And heterogeneous watershed may be divided into sub areas with different numbers and then we can get a weighted curve number and then we can get the curve number for the local condition depending upon the soil and other conditions. So, this here you can see that rainfall in x axis rainfall p in millimeter and the direct runoff q. So, here a infiltration curve is also drawn and then the curve number is obtained from this and the curve number we can easily identify from this the charts which is available in most of the hydrologic test book which is developed by soil conservation service manual 1972. So, now say before closing this lecture. So, one example problem calculate the runoff from a watershed of 50 hectare for the following data using a CSCN methods. So, depth of rainfall is 150 mm and this and moisture condition is AMC 1 crop good condition 30 hectare and good land and good condition 20 hectare. So, here type of crop and curve number is given. So, we can find corresponding AMC 1 condition from this. So, you can see that a weighted curve number we can identify based upon this as 53.66 and then we can identify what is the curve number using this equation and then we can obtain this s value which is the storage is equal to 219.35 for this problem and then directly we can obtain the runoff q is equal to p minus 0.2 s whole square divided by p plus 0.8 s. So, q we can obtain this for this problem 34.606 millimeter. So, here the rainfall is 150 mm. So, corresponding runoff for the watershed will be for the area will be 34.606 millimeter. So, like this we can solve this type of various type of problems. So, even though say this model is developed CSCN method is developed for American watershed. We can use this for various conditions and we apply this method for various countries at various locations and then we can modify the curve number also by considering the various aspects of the watershed or area which we consider. So, nowadays for the given conditions say for example, India is concerned we can develop the curve number for our local conditions. So, for today's lecture these are some of the references used and before closing the lecture some one tutorial question study the different types of models used for runoff calculation for a given rainfall. Compare the black box model, number of models and physically based model with advantages and limitations of each. So, for a typical watershed compare various empirical equation available in literature for the calculation of runoff and for a given rainfall depth calculate the runoff using each method and compare the results and get necessary standard value for each method from the literature. So, this tutorial you can do based upon today's lecture and some of the references given and if you self evaluation questions why models are required for watershed planning and management. Differentiate between black box models, number of models and distributed models and what are the important model selection criteria in watershed modeling then discuss the important empirical equation used for runoff calculations for a given rainfall. So, all these questions you can answer based upon today's lecture. Then few assignment questions like which are the different processes that can be simulated using models in the watershed. Then differentiate between even based continuous lumbered and distributed models. Then illustrate the rational method for runoff estimation with its advantages and limitations. Describe the SCN method for runoff estimation with its advantages and limitations. So, all these questions you can easily answer through by going through today's lecture. Then one unsolved problem for your watershed area for a given rainfall depth calculate the possible runoff using rational method SCN method and compare the results from the topographic and land use details obtained the runoff coefficient for various areas find the average runoff coefficient based on literature values. Based on the land use pattern and possible land use moisture condition identify the possible current number and get the weighted average then compute the runoff based on the average runoff coefficients and current number. So, this you can easily do for your area. So, now today what we discussed is various hydraulic modeling approaches. So, we have discussed in detail about the empirical equation of black box models and the lambda models. So, in next lecture we will be discussing the distributed models by considering the given equation and other aspects. So, we will be discussing the physical models in the next lecture. Thank you very much.