 Namaste and welcome back to the video course on water shed management. In today in module number 7 on management of water quality, lecture 29 we will discuss about the water quality modeling. So, some of the important topics covered in today's lecture includes water quality protection, water quality goals, hydrodynamics, transport processes, oxygen regime, mathematical modeling, governing equations, numerical modeling and ground water transport modeling. Some of the keywords for today's lecture include water quality modeling, hydrodynamics, mathematical or numerical modeling, ground water transport. So, as we were discussing earlier say water quality is a major issue when we deal with the water resource in a water shed. So, it is not only the quantity of water which we have to get for the various purposes, but the quality for various purposes like bringing water say domestic usage or irrigation or industrial certain specific qualities to be matched or certain standards to be matched like your World Health Organization standards or Indian standards or British standards like that. So, that way we have to say as we discussed in the previous 2-3 lectures we were discussing about the various sources of pollution for surface water, ground water then various issues related to that we have already seen in the last few lectures. So, when we deal with say particular area like a water shed say as we have discussed it can be the pollution can be surface on surface water or the ground water pollution. So, we have to study in details what will be the say the present status say when we are looking the particular aspect what is the present status where which area the area is polluted say like a ground water or surface water, what are the types of pollution, where is the source of pollution and then what type of measures we can adopt to control this pollution and then what kind of remediation can be done. So, though all those aspects we were discussing in the last few lectures. So, as we have seen this when we deal with the surface water quality or ground water quality say we have to always see the water quality say the it is within the perspective of say what is the spread of the pollution or say where it is moving further so like that. So, that way water quality modeling is very important. So, water quality modeling means say it is say through mathematical or various types of models we are trying to say how the within a system like in a control volume or within a domain how the pollutant is or the contaminant plume is moving or how the behavior within the system. So, that is what we are trying to study say when we say about water quality modeling. So, that can be either surface water quality modeling or ground water quality modeling. So, I will say let us look into the various aspects of this water quality modeling. So, water quality models as we already discussed simulate the fate of pollutants and state of selected water quality variables in water bodies. So, like it can be a total resource solids or the COD, VOD. So, what type of parameters we choose accordingly the we can develop the water quality model. So, this type of water quality models incorporates variety of physical, chemical and biological processes which control the transports and transformation of these variables. So, within the say when we can say watershed say either in surface water or ground water this the contaminants or the plume that will be moving from one location to another location with the movement of the water. So, how say this movement is taking place or how we can control the transports and transformation. So, that is what we are trying to do through water quality modeling. So, various parameters like a temperature, solar radiation, wind speeds, pH, light and air attenuation coefficients. So, so many parameters can control say the type of the the the the contaminant movement or pollutant movement within within surface water or ground water within a watershed. So, that way we have to see the the pollutant loading within the watershed. So, which direction say how much pollutant pollution pollution is there and which direction it is moving within the surface water or ground water. So, that way each water quality model has its own set of characteristics and requirements. So, depending upon what type of parameter we are trying to model. So, we have to develop specific type of water quality modeling either for surface water or ground water. So, depending upon what type of way we are trying to model the system. So, that way each water each water quality model has its own set of characteristics and requirements. So, some models can be applied to several types of water bodies and some models only for particular water bodies. So, the model can be specific for particular cases or we can develop generalized models. So, that can be applicable to most of the problems. So, it can be like say nutrient models or the the algae movements or the TDS within the surface water or ground water. So, like that we can consider say particular type parameters and then its behavior and its transport or its movement within the aquatic environment either in surface water or the ground water. So, within this perspective when we say about the water quality modeling we can have different types of water quality models. So, water quality is modeled by one or more of the following formulations. So, it depends upon what kind of as we discussed what kind of pollutant or contaminant is there and then what is the process of movement or how the behavior of that particular system within the particular control volume or particular domain. So, that way we can have advective transport formulations. So, where mainly the advection. So, with this we already discussed about advection. So, how the movement is taking place. So, advective transport formulations or we can have dispersive transport formulations within the surface water or ground water and then wherever say if heat is the main source of pollution like say the hot water coming from thermal power plants to the lakes or to the ocean or to the rivers. So, we can see how the heat transport is taking place. So, that way we can have heat budget formulations or say we can also study the issues related to water quality related to dissolved oxygen condensation and then whether it is decreasing or increasing and then if you go for aeration how it is how we can re-array it and then how much saturation can be achieved how saturation can be achieved like that. And then also we can have a different types of water quality models related to carbonaceous deoxygenation or COD or sediments say movement and related modeling or biochemical oxygen demand modeling or pH then alkalinity the nutrients then algae and or the microorganisms within the surface water or ground water. So, that way depending upon what type of parameter we are trying to model or depending upon what kind of contaminants we are trying to say study within the watershed or within the particular area. So, that way we can have a specific type of water quality model. So, like adductive transport model or with respect to the processes or like sediment transport modeling or say nutrients trans modeling. So, like that. So, then as we discussed earlier also say the when we consider within the perspective of watersheds. So, watersheds is an area as we discussed with specific boundaries within a hydrologic system. So, that way the main source of say water is rainfall and then surface runoff and then infiltration ground water and then finally, this water through river will be moving to the ocean. So, that way say when we deal with the water quality modeling. So, we have to see that what kind of say things coming to the to the watershed or say or what kind of things will be going out of the watershed. So, that way when we deal with the water quality modeling within the perspective of hydrologic cycle or within the perspective of a watershed we have to deal with emissions that means, what is coming out of say like from the users point of view like from the community what is emitted or what is coming out like a sewage or from the factory what kind of effluent is coming. So, like that emissions. So, avoidance and reduction of pollution into the environment. So, that is generally what we will be discussing in this related issues. So, like in sanitary engineering or environmental engineering and then another thing which we have to generally deal say within the watershed perspective is emissions that means it into coming into the system like from the water bodies point of view say what kind of say polluted water is coming to the system and then consequence of pollution then injection etcetera. So, that way now a new branch of fluid mechanics has been involved in the last few years. So, generally it is named as environmental fluid mechanics. So, where we are trying to study or we are trying to model the behavior of various pollutants and then say its behavior within the system like a control volume or within the domain we consider and then say the flow and transport in surface water like rivers and lakes, flow and transport in soil and ground water, flow and transport in the atmosphere. So, like that a new say branch of engineering or fluid mechanics has come which is called environmental fluid mechanics where the various issues related to transport behavior within the water soil and airy air are discussed. So, within the perspective of water quality say we will be discussing say what we will be the behavior of particular contamination within a river lake or pond like that as far as surface water is concerned or within the within ocean also and then ground water is concerned what happens within an aquifer environment how the pollutant is moving. So, all those issues we will be discussing within the perspective of the hydrologic cycle. Then say when we consider say the water quality issues related to in the perspective water cycle. So, like say the water is say supplied from surface water source or ground water source and then it will be taken for domestic purpose, industry purpose or trade purpose or various other purposes. And then this intake will be restricted through various laws and then say after this industrial trade or domestic processes then a fluid will be there and so within the process engineering whatever we can do the treatment all those things. And then finally, say the sewage water or storm water is coming say as storm water wastewater and then that is again coming back to the systems say like receiving water body like rivers, lakes or ocean and that also affect the ground water system. So, that way it is we can say that the water quality issues are also related to water cycle. So, since water is taken from surface water, ground water sources and after specific usages it is coming back to the system as either treated water or in sometimes a fluence or with some condemnation. So, that way we can say that when we deal with water quality modelling, so say these issues are related to the water cycle. So, now when we deal with water quality modelling say we have to see the say what kind of protection measures we are looking for and then what are the aims or what are the goals which we have to set say for the particular watershed or particular issues are concerned. So, these are some of the important questions which we may have to answer generally. So, as far as water quality protection is concerned generally we are trying to ensure the quality of water which guarantee the preservation of environmental goods. So, as we already discussed earlier, so the water quality say in terms of surface water or ground water say within the perspective environmental goods we can say that this is the standard which we are looking for the treated water coming to a lake or to the river. So, like that we have to say the water quality protection since the existing water within the river we have to protect with respect to the outside water coming, the wastewater or the treated water coming to the aquifer systems. So, that to the river systems or the aquifer systems wherever the interaction will be taking place. Then say when we look into the environmental goods, so it is just like the functions of the river as water resource then community of aquatic living then fishing then irrigation of farmland and then say for leisure and creation purpose. So, we have to say as far as condemnation is concerned the various standards are there and various goals we have to set and then we have to say the substances from inland and suspended solids and sediments then especially for drinking water is concerned we have to see the overall the best quality water is required for drinking water purposes. So, that way we can set the environmental goals or environmental goods with respect to specific usage and with respect to the available sources we can set either for surface water or ground water. And then as we discussed most of the time there will be interaction between the surface water and ground water. So, if the surface water is affected like rivers, lakes or ponds are affected then that also automatically may affect the ground water system. And so, when we look into the water quality goals, so water quality goals are given as a concentration of the substance say like the TDA should be less than 500 ppm or the fluoride should be say within the range of 2 ppm. So, like that various quality goals we can set. So, this water quality goals shows condition of say for example, if we consider river with regard to the environmental goods then function as an instrument for decisions, protection and improvement of water quality. So, these are generally derived from effective values and laws. So, as far as the water quality goals are concerned for various countries or various standards say various quality goals will be set. And this depends upon the various environmental regulations then the specific water usage and then the location of the area. So, like that many parameters are there to set specific type of water quality goals or water protection, water quality protection measures. So, that all this depends upon various parameters. So, when we look into water quality modeling say various considerations which we have to concentrate with respect to the various substances within the water. So, as we discussed say due to the various source of pollution so as far as water is concerned the substances within the water can be either dissolved substances or emulsified substances or particles within the water. So, as far as dissolved substances are concerned say it can be either hydrodynamically neutral like a simple tracer or hydrodynamically active like it can change its phase like density or viscosity all those things can change. So, it can be like salt water within the fresh water or various chemical say fluids within the water. So, water substance can be either dissolved or it can be emulsified like drops or bubbles say like a lather or other kinds of contaminations. And as far as particles are concerned it can be suspended materials like sediments coming from watershed or wet material and then other kinds of sediment things within the flowing water say like in river or within the watershed of overland flow or the channel flow say wherever these particles will be eroded and then that will be sometimes will be within suspended way or it can get settled with respect to the various environmental conditions or with respect to the velocity of the flow and other conditions. So, when we look into the water substances we can say divided into dissolved, emulsified or particles. So, now when we look into water quality modeling say as I mentioned we are saying we are trying to depict this the various parameter behavior or movement in terms of mathematical laws. So, that generally we can use the governing laws as conservation laws most of the time we use the conservation laws like conservation mass, conservation of momentum, then the conservation of the energy or heat and then the substances in water. So, like that the conservation laws we can consider like a conservation mass, momentum and energy. So, when we try to when we are trying to develop the mathematical models we can consider either micro scale or macro scale. So, micro scale like an elementary control volume we can consider a control volume like dx into dy into dz of size like this or it can be on macro scale like a section between two section between in a river or within a pond or lake. So, it can be either control volume can be elementary size or it can be macro scale. So, now when we are trying to say most of the time water quality modeling is concerned we will be trying to develop mathematical models since that is the way we can try to quantify say the contaminations or the pollutant movement within the aquatic environment either surface water or ground water. So, mathematical models say first we are trying to set in terms of certain govern equations and boundary conditions and initial conditions and then say it can be the with respect to spatial variations like one dimensions, two dimensions or three dimensions and then it can be time dependent or time independent. So, it can be steady state or transient variations. So, otherwise say if you want to look in a holistic way as far as water quality is concerned with respect to the measurements we have said various location that is a quite cumbersome and very expensive process. So, that way we are looking to the mathematical modeling. So, mathematical modeling as far as water quality is concerned that tries to give the to use the prediction of water pollution using mathematical simulation techniques. A typical water quality model consists of a collection of formulations representing physical mechanisms that determine in the position and momentum of pollutants within the water body. So, as we discussed like say the govern equations are generally coming from conservation of mass, momentum and energy. So, that way this specific models are derived mathematical models are derived and these models are available for individual components of the hydraulic systems such as surface runoff or ground water systems or various specific type of say reactive transport or specific components of the pollutant is concerned. So, these type of models are addressing the hydraulic transports and for ocean and exurean applications. So, transport can be as far as within the surface water environment like lake, river or pond or ocean and then also it can be within the ground water systems. So, that way also possible. So, that way as far as water quality modeling is concerned we first try to represent the particular say pollutants or contaminants within the environment in terms of mathematical description like governing equations and the boundary conditions. So, in this way when we are trying to develop the water quality models say as we discussed various processes like say diffusion, dispersion, advective transports, reactive transport like that what we discussed in some of the earlier lectures. So, that way we have to understand the hydrodynamics what is happening within the surface water or ground water. So, that way say how the flow is taking place the depth variations with respect to space and time and then velocity variations, pressure variations etcetera. So, we have to first understand the hydrodynamics or the mechanism of flow within the domain or within the environment which you are considering. So, that way we have to do first a hydrodynamics modeling and then we will be going for the water quality modeling or transports modeling. So, hydrodynamics is concerned generally we can represent the governing equations in terms of conservation of mass and then conservation of momentum or a conservation of energy. So, conservation of mass generally so called continuity equation we can derive as shown in this equation. So, here v x v y and v z are the velocity components in x y is a directions, rho is the density and t is the time. So, this we can derive say when we consider the time variation and the density variation. So, if you are considering say for example, like water we consider as incompressible fluid then this equation converts to the continuity equation like this where del v x by del x plus del v y by del y plus del v z by del v z is equal to 0. So, that way we can derive the continuity equation based upon the conservation of mass. Then say the other types of equation which we have to generally solve is the equation based upon the conservation of momentum. So, generally these equations are called Navier- Stokes equations. So, in three dimensions we can have governing equations in x y z direction. Say for example, in x direction the velocity the with the velocity variations in x y directions are represented as v x v y and v z and then g is accession due to gravity and h is the flow depth and then nu is a kinematic viscosity. So, then this equation say we can represent say for example, in x direction and del v x by del t plus v x and del v x by del x plus v y into del v x by del y plus v z into del v x by del z is equal to minus g by del x plus nu into del square v x by del x square plus del square v x by del y square plus del square v x by del z square. So, that way we can represent the momentum equations. So, this for x direction similarly we can write for y directions and z directions. So, generally we can solve to understand the hydrodynamics within the domain we can solve the continuity equations and the momentum equations say these three equations in for 3D problems and the continuity equations. So, from that generally we can obtain the velocity variations and the pressure or depth variations within the domain or within the location or within the area which we are considering. So, the modeling can be 3 dimensions or 2 dimensions or 1 dimensions depending upon the various consideration which we are trying to model the system. So, then say this gives the solutions of this continuity and momentum equations give the variations of the velocities and the depth or the pressure variations within the flow domain. Then say various say as far as transport is concerned we have to consider various processes like diffusive process like molecular diffusion and turbulent diffusion and dispersions. And then say if molecular diffusion is concerned it is the transport process that originates from the molecular activities like a Brownian movement and then the driving force for molecular diffusion is the concentration gradient. So, wherever the gradient is there wherever the concentration is higher then it will be moving towards low concentration gradient. So, that is so based upon so called fixed low fixed first low. So, the molecular diffusion is generally described by the molecular diffusion coefficients as shown here and fixed low is represented as Q is equal to minus dm del C by del x where C is the concentration and dm is the diffusion coefficients. So, that way based upon this fixed low we can derive the mass transport equation same for a for a control volume by considering the convective transport also. So, this the governing equation generally say this also we can write in x y z direction. So, here a specific same specific equation for mass transport x y z direction is specifically for the hydrodynamics and mass transport equation is only with respect to the variation in x y z direction as shown in this equation. So, that is v x in del C by del x plus v y into del C by del y plus v z in del C by del z minus dm in del square C by del x square plus del square C by del y square plus del square C by del z square is equal to minus del C by del t. So, this gives the mass transport equation say the variation we can get in x y z direction by solving this one equation and then of course say v x v y v z we are obtaining from the solution of the concentration of mass or continuity and momentum equations as described in the previous slides. So, then if you are trying to model say the heat transfer problems like as we discussed this say related to the heat transport processes which we have to consider then we can solve the governing equation can be obtained like this and then say this dt stands for thermal diffusivity coefficient and T is the temperature and v x v y is the velocity variation. So, this heat transfer equation we can solve. Then say if the say depending upon the flow conditions say the flow within the aquatic environment like in a lake or say river say or in a channel the depending upon the velocity of the flow it can be turbulence or the laminar. So, this we can define in terms of so called Reynolds number say that Reynolds number variation we can consider and then in terms of Reynolds number give the ratio initial force to viscous force. So, we have to identify first is the turbulent flow or laminar flow accordingly if that it is flow is turbulence and we have to consider the turbulent nature of the flow. So, nature of turbulence like irregular characterized by variations with respect to time. So, this is happening due to intensive mixing rotation dissipative movements like that. So, you can see that if it is laminar flow then the velocity variation will be in layers or the flow will be in terms of layers. If it is turbulent flow you can see that the velocity variation is the flow is fluctuating or the velocity is varying like this. So, that way when the turbulent flow say as far as the transport process is concerned we have to consider the variation with respect to mean variation. So, v is equal to v bar plus v dash. So, v is the velocity vector. So, v bar is the mean velocity and v dash is the fluctuating component. So, similarly the pressure variation or the various other parameters we can consider as far as the turbulent flow is concerned. So, then say in a turbulent flow also we have to solve the continuity equations and momentum equations. So, the continuity equation with respect to mean component the same way we can write. So, this is this is this is the equation and then the momentum terms the from the Navier-Stokes equation we can say transform with respect to this fluctuating components and the mean components and then the final equation can be written in this. So, these equations you can see in any of these standard fluid mechanics like fluid mechanics by Wiley and Streeter. And then say as I mentioned say the the main important parameter which we governs whether the flow is laminar turbulent is the Reynolds number which is the ratio of inertial force to viscous force. Say for example, pipe flow the flow will be laminar up to the Reynolds number of 2000 and 2000 to 4000 we consider as the the say the variation is transformation is taking place to laminar to turbulence. So, above 4000 it will be completely turbulence. So, but up to 2000 generally we model as laminar variation laminar flow conditions and above say 2000 say or say definitely above 4000 it is turbulent, but above 2000 say the transformation is from laminar to turbulence. As far as upper general flow is concerned say up to 500 we consider as laminar and above that we consider as turbine flow conditions and then the we have to use the specific type of equations for laminar flow conditions or turbulent flow conditions. So, the turbulent flow condition say say the momentary equation which is derived from the say the same the Navier-Stokes equation which is generally called as Reynolds transport equation is described in terms of the fluctuating component of velocities like V x dash V y dash and V z dash and its variations. And here this eta is the kinematic viscosity which is defined as say dynamic viscosity eta by rho. So, nu is equal to eta by rho. So, in terms of that we can represent. So, that way when we are looking for the the the water quality modeling. So, first we have to solve the hydrodynamics and then obtain various parameters like flow variations, pressure variations or the velocity variations either in laminar flow conditions or turbine flow conditions. Then we have to solve the transportation like advective transportation which we have mentioned. So, the solution of this transportation is only possible once we know the hydrodynamics or the flow variations. And then when we solve this say hydrodynamics equations or flow equations and transport equations together we can get the flow variations as well as the transport variation within the the domain which we consider. So, as far as water quality modeling is concerned as we discussed the various important parameters which we have to consider are the molecular diffusion, turbulent diffusion, dispersion, momentum flux, turbulent moment exchange, heat flux etc. So, these various terms are quantified as shown here. So, like a diffusion what is happening or dispersion within a river or turbulence and all this we have to consider when we look into water quality modeling. So, anyway going to the all the details of this is not the purpose of this lecture since now we are discussing water quality issues relevant to watershed modeling watershed base only. So, that way we are not going to all these details of this kinds of water quality modeling. So, now say as far as water quality modeling say for example, transport in rivers and canals are consensed say for example, one dimensional transport. So, if you consider the convective transport or dispersive transport. So, the governing equations which we have to solve is shown here where here u is the velocity, c is the concentration and a is the area of flow then say k is the dispersion coefficient. So, like that we can consider a control volume like this and then we can do the water quality modeling. So, like a size of section microscopic or microscopic. So, these details are taken from the lecture notes of Professor Kobus Department of Civil Engineering University Stuttgart Germany say what the course notes on environmental food mechanics. So, like a distribution process diffusion then we have to consider say like this which is coming from the fixed law and then say microscopic dispersion all those things we have to see the convective transport behavior also within the system we consider. So, the modeling is consensed say for example, say the contaminant transport within river or a channel say as I mentioned the modeling can be in one dimensions one dimensional modeling or two dimensional modeling or three dimensional modeling. So, accordingly the governing equations here is given. So, this is say for example, one dimensional modeling del c by del t plus v x and del c by del x is equal to k into del square c by del x square k is the dispersion coefficient where i is the sink or source stem. So, like that we can represent similarly if you are considering two dimensional transport water quality modeling. So, we have to solve the equation in x and y. So, this equation will be a governing equation and then three dimensional transport equation will be with respect to v x, v y, v z and this terms we have to solve the system say coupled with the flow equations of continuity equation and the moment equations. So, that we are depending upon what kind of say water quality modeling you are intended to do say like in the transport phenomena or the contaminant transport in a river in a lake or whatever system which you are considering. So, we can go for one dimensional modeling say for example, river quality modeling generally we can do one dimensional modeling or two dimensional modeling or three dimensional modeling. So, now another important aspect which we generally will be looking to is the oxygen regime of rivers when we are looking for the river quality modeling. So, this we can represent in terms of dissolved oxygen. So, the combination of oxygen deficit and re-aeration we can combine in terms of an equation called a Streeter-Felds equation. So, here the assumptions used in the derivation of this equation include oxygen transfer only over water air interface upstream effects are not taken into account. So, governing equation is del C s minus C bar by del T is equal to k D into L minus k A into C s minus C bar where this parameters like L is the biological oxygen demand, L 0 is the biological oxygen demand at time T is equal to 0, then k A is the coefficient of re-aeration, then k L is equal to R by Y, k D is the decay coefficient C s is the oxygen saturation concentration. So, like that and with respect to certain boundary conditions with respect to this concentration of dissolved oxygen and the by BOD particular conditions we can identify the oxygen regime within the river. So, you can see that if say oxygen say with respect to time in days if you consider particular location. So, oxygen saturation is this and then say if depending upon the contaminant pollutant load within the river the oxygen profile if there is no aeration is taking place then it will be keep on decreasing like this and then if there is aeration we are giving or aeration is taking place then oxygen profile with aeration is shown this as shown in this figure as reproduced from the lecture notes of professor Kobus. So, say as far as street or fell situation is concerned we can even have an analytical solution as given here. So, when we are looking for the the modeling of oxygen regime within the river we can use even this street or fell equations and then correspondingly we can identify how the oxygen content changes within the particular section or within the same longitudinal section of the river. Then another aspect you say as we discussed is the water quality is concerned it can be the surface water or ground water. So, this ground water transport is also we have to model with respect to the flow and transport phenomena. So, the say for example, when we consider two dimensional flow and transport modeling there are many equations say in a confined aquifer and we can write like this del y del x of T x in del h by del x plus del y del y of T h in del h by del y is equal to s in del h by del t plus q w in delta index minus x i y minus y a minus q s. So, similarly the same thing this T x T y are the transmissivity of the aquifer system k x k y are hydraulic conductivities. So, similar way the equation we can write for unconfined aquifer and q w is the pumping say at particular location and q s is the source sourcing terms within the aquifer systems and based upon this flow equations we can solve this equations based upon the appropriate boundary conditions and initial conditions and then we will be getting the head distribution within the aquifer systems and then using the Darcy's law we can get the velocity variation v x and v y as shown here. Then we can put this v x v y in the transport equation which is given here where r is the retardation coefficient generally we can consider as that is equal to 1 if there is no retardation effect to be considered. Then dx and dy are the dispassion coefficients v x v y are the velocity obtained from here and then c is the concentration and lambda is the radioactive decay coefficients. So, like that depending upon what type of parameters we will be modeling as far as groundwater is concerned and we can use the groundwater transport modeling. So, as far as water quality modeling is concerned we can say look into surface water quality modeling or groundwater quality modeling and then for specific same processes we can have specific type of mathematical equations or models or specific components like TDS or BOD COD or nutrients or algae or microorganisms we can have specific set of equations. So, we will be solving this type sets of equations and then we will be trying to get a solution as far as the flow and transport process is concerned. Then say while solving this type of equations as you can see these are all partial differential equations. We cannot only few specified cases simple cases only we can have the analytical solutions. So, for most of the field problems we cannot have the analytical solutions. So, that way as we discussed earlier also we have to go for numerical modeling. So, numerical procedures gives the approximate solution to most of the field problems. So, this numerical models transform a complex practical problem into a simple discrete form of mathematical description and these numerical models recreate and solve the problem on a computer and finally reveal the phenomena virtually according to requirement of the user. So, numerical approximate solutions for a complex problem efficiently as long as proper numerical method is used. So, there are number of numerical methods are available with respect we say for the last few decades with the advancement in computer technology number of numerical models like a finite difference method, finite element method, finite volume method, method of characteristics, boundary element method, mesh free methods like that number of techniques have been developed. And then depending upon what type of process we are trying to model or what kind of say contaminant we are trying to model within the aquatic environmental either surface water or ground water we can choose specified models, specified technology and then of course nowadays large number of models are available in the market. So, depending based upon various numerical techniques like finite element method or finite difference method which are the most commonly used numerical tools. So, we can choose depending upon the users familiarity and needs we can choose particular same models for surface water quality analysis or ground water quality analysis. So, as far as surface water quality models are concerned few of the most commonly used models I have listed here. First one is the WASP water quality analysis simulation program it is by United States State Environmental Protection Agency. And this WASP interpret and predict water quality responses to natural phenomena and man-made pollution for various pollution management decisions. Then another model is called QAL 2K quality 2K. So, these models we can use for river and stream water quality models either 1D or 2D. And then another model is called aquatox. So, this model is used for simulation of aquatic systems it predicts the fate of various pollutants such as nutrients and organic chemicals or a effects on ecosystems. And then another model EPUD1 so, riverine hydrodynamic and water quality model a system of programs to perform 1D hydrodynamic hydraulic water quality simulations. And then the famous SWM model storm water management model where the hydrodynamics and the transport within the open journals we can simulate. So, so called SWM models. So, like that large number of surface water quality models are available in literature and in the market. So, depending upon what type of problem we are going to solve and then what kind of condemnation you have to address we can choose a specific type of models. Then as far as groundwater quality models are concerned for flow modeling we can use this the standard model based upon final difference called a mod flow. Then which is given by United State Geological Survey USGS, then mod path flow line model for depicted streamlines and MOC USGS 2D advection dispersion code, then MT3D 3 dimensional transport code with which is which works in conjunction with coupled with a mod flow. Then RT3D 3D transport say reactive transport models and this also works with a mod flow. Then bioploom 2 and 3 related to the bioremodation modeling. Then finite element based models like a FEM water, then number of other packages like groundwater modeling systems you can see. So, here also as far as groundwater quality modeling is concerned depending upon the type of model which you are looking for 1 dimension, 2 dimensions or 3 dimensions and depending upon the contaminant which we have to address. So, we can choose specific type of models and then we can use for the groundwater quality modeling. So, now before closing this lecture say we will briefly go through how a specific type of groundwater quality model can be used to predict the transport phenomena transport within an aquifer system. So, the case study is in Belgam area. So, this is the aquifer system the domain area. So, this area say one of my student Meenal has modeled using the mesh frame model which she has developed. So, the details of this study area is given in Thoretel 1999 and then Meenal and Ldo submitted to the hydraulic engineering SE. So, some of the parameters considered in this study area the watershed area the aquifer area say about 72 square kilometer and this is basaltic terrain say on north end side of Belgam. Then watershed is drained by a river called Markandaya river in the north and here the main source of pollution is Red Mud, Hydro Silt Muddy highly alkaline solid waste produced by physical and chemical treatments of bauxite industry in this particular location. So, main source of pollution is TDAs coming from this. So, Red Muddy is harmful to the ecological environment safety of its storage has become an environmental problem. So, the natural recharge in this area 65 millimeter per year as estimated by National Geographic Research Institute NGRI. Then say this seepage from Red Mud Pond is simulated as additional recharge about 130 mm per year. So, as far as the aquifer system is concerned in the model for modeling purpose we have considered three zones. Zone 1, zone 2 and zone 3 as shown here this is say this one is say zone 3 is this zone 2 here and then zone 1. So, here this is the Markandaya river on the sides. So, here the longitudinal dispersivity is considered as 50 and trans space this space 50 as 5 and specific yield of the aquifer is considered as 0.2. So, for zone 1 the hydraulic conductivity is 0.5 meter per day zone 2 1 meter per day and zone 3 2 meter per day. So, as I mentioned my student Meenal has developed a mesh free model the details are given in this conference paper as well as this submitted journal paper. So, this is the domain which we consider the mesh free model. So, this is the the contaminant existing plume our aim was after 10 years how much the contamination will be spreading. So, here we developed a flow model and the transport model based upon the mesh free technique. So, here the various nodes we simply use only nodes. So, the details of this mesh free technique you can look into this paper in the journal engineering analysis with the boundary elements published in 2012 two dimensional contaminant transport modeling say using mesh free point collocation method. So, here this way this is the aquifer domain and these are some of the nodes used for the modeling and this is the existing plume. So, using say flow and transport 2D we considered 2D model. So, this is say the steady state head distribution within the aquifer system varying from say 755 meter to 720 meter. So, here this is the river flow and this is the head variation and based upon this the velocity distribution has been determined by running the model the coupled flow and transport model. Then the head distribution after 20 years. So, this model has been run for 20 years and then you can see the the various the the head variation within the aquifer system after the the simulation for 20 years. So, this is 755, 750, 745, 740, 735, 730, 725, 720 and like that we identified with respect to the some of the abstraction taking place within the the domain with respect to certain pumping wells existing in the aquifer system. And then after 20 years of the simulation how the the contamination is spreading. So, you can see that this is the existing contamination say with respect to the the the 1999 data. So, then after 20 years say how the contamination is spreading you can see that here small movement the hydraulic conductivity is very low in this area. So, the contamination spreading is very small as you can see here. So, the main purpose of the presenting this case study is to show how this type of models we can develop as far as the flow and transport either in the the ground water systems or the surface water systems also we can develop such models. So, generally we have to solve the flow and transport models together. So, flow models give the variation of velocities and depth variation or the hydraulic the depth the the hydraulic potential within the aquifer systems as far as ground water is concerned. And then based upon that say we can identify how the velocity variation is taking place. And then we solve the the transport equation either in 2D or 3D or whichever way we are modeling and that gives the the variation of the particular constituents like TDS or that concentration how it is moving say spatially as well as well as temporarily. So, that is the way we do the water quality modeling either for surface water or ground water. So, some of the important references used for today's lecture say especially the websites www.pa.gov where environmental protection agencies website and some of the other literature used for today's lecture. So, before closing some of the questions like tutorial questions critically study various ground water and surface water quality models available in literature. So, we can see the various models available like in EP website or Bentley website study the capabilities of each model and the the problems where it can be applied. So, some of the models we have already discussed and then other models details we can you can get from the internet sources. Then some self evaluation questions evaluate the different types of water quality modeling and describe water quality modeling within the perspective of water cycle. Explain various conservation laws used in water quality modeling and describe with governing equations in the ground water transport modeling illustrate the role of numerical modeling in water quality modeling describe various models used in water quality modeling. So, all these questions you can answer based upon today's lecture and then a few assignment questions like illustrate watershed based water quality issues within the perspective water hydrologic cycle and what are the typical water quality problems goals then describe with governing equations the surface water transport modeling then illustrate the oxygen regime modeling in reverse or in channels then describe various models used in surface water quality modeling. So, all these questions also you can answer based upon today's lecture. Then say some unsolved problems say with reference to typical point source pollution from an industry to ground water in your watershed area critically study the possible water quality modeling for TDS concentration identify the possible water quality model from the open sources making mode floor empty 3D then collect the necessary data for the water quality modeling and try to develop the model for your study area and predict the future spreading say for next 10 years or 20 years how the the transport is taking place contaminant transport is our plume movement is taking place within the ground water systems. So, what we discussed today is say mainly on water quality modeling. So, we discussed about the surface water quality as well as ground water quality. So, we discussed the mathematical governing equations and then say how we can say model say typical systems say either in one dimension two dimensions or three dimensions. So, we will be further discussing one more lecture on the water quality modeling related to environmental guidelines as far as the water quality issues are concerned in the next lecture. Thank you.