 Hello. Welcome to rural water resource management NPTEL course week five lecture five. So the past lectures we have been looking at the groundwater hydrology components and we have looked at specific most important parameters of porosity, permeability, hydraulic conductivity, specific yield, specific retention, etc. We will be wrapping up the groundwater hydrology component part this week. And I do hope to recap so that we can link all the different lectures together. So in this lecture, let's do the recap and also try all these parameters together. But before that, as I promised, we will look at hydraulic conductivity and variations. We would also probe the reasons for such variations. Let's take the first example. As I mentioned in the previous lecture, there is a big range for hydraulic conductivity properties. And I'm just talking about one dimensional. So let's take one dimension, let's say vertical along the z-axis due to gravity along the gravity. We do have a range for each hydraulic conductivity associated soil material. So for example, if you have it to be soil on consolidated deposits, which means it has been deposited or it has been weathered, those kinds of things, whereas rocks are still the parent material and from which weathering can happen. So you can divide it into two, but we'll focus here because this is where farming happens and rural water management happens. This would be mostly on the deep wells and those kind of things that we need to understand the hydraulic conductivity in those regions. Since we are not dealing with massive irrigation projects for rural, we'll be looking at this part. Okay, so let's take one example of silty sands and loas. These are kind of the combination of different materials in soil, different textures and different sizes, which is mostly common in nature. You won't have one specific type. You could have that only in, for example, desert is purely sand, clean sand, and then gravel is along the riverbeds or along the Himalayan regions where erosion happens. So all these rocks are part of the mountain and then erosion happens and then they start to move down. When they start to move down, they become round because the edges are broken while they are transported and that is why you see a pebble or gravel, everything is shaped round. It's not sharp, but if you break it off, it is sharp. Okay, so water takes it along and on the way, it actually shapes it into a round object or a spherical object, a very smooth object. Okay, so coming back, let's go to silty sand or silty loases and you could see that the range. Let's take from here. It ranges from your hydraulic conductivity centimeters per second, 10 power minus 7 to 10 power minus 3. And this is because hydraulic conductivity is a function of the soil medium and also the fluid. So the fluid, we might assume it is just water. So let's say, okay, we're just looking at water, so we know the density, viscosity of water, etc. But your hydraulic conductivity is an intrinsic property of the soil material also. And here the soil materials, porosity influences the connectivity of the pores, influences the permeability, the permeability of the soil to allow water to flow is different. Okay, so keeping in mind all these, which are mostly on the management side, only some properties for hydraulic conductivity are natural properties like texture of the soil. But the other things like porosity and you have the connectivity of pores, all those are kind of managerial. Whereas your permeability, resistivity, all those things would be more in the texture class. So let's move on. And as I promised, I would do a comparison of hydraulic conductivity at annual scales. We saw these kind of like a velocity, okay, how much easily water flows through. It's not called as a velocity per se, but it is the measure of how easily water flows through. And it is a flux rate. Okay, so and it is given as a unit distance per unit time, so centimeter per second. Let's take that unit from the previous lectures and books. What you find is you can easily do this on your Google calculator, or you could use your books and calculate, etc. For learning purposes, I'm showing it in Google calculator. Okay, so one centimeter per second, two kilometer per year, that's all I put. You can change the number one to nine, etc. But here, the values range from one to a 10 power minus two, and then play is 10 power minus nine to 10 power minus six. Taking the extreme values in both cases to show how big it is. If you see the first part, the gravel, one centimeter per second is equivalent to 315 kilometers per year. So if you drop your water in the Himalayas with all gravel, within a year it transports itself, it flows across 300 kilometers along the gravel, and mostly your gravel is on the top. If it gets to the bottom of your gravel bed and you have a lot of gravel, then also it can flow. That is why you see under the mountainous regions, you do have rivers that flow. And that those rivers are fed by these groundwater, which comes into gravel structures. Moving on, let's take the clay example, and you'll be surprised that 10 power minus nine, eight zeroes into one, is equivalent to 0.3 millimeters per year. So you're not even moving a centimeter in a year. Okay, so if you take clay and groundwater into the clay layer, you're recharging it through rainfall or your imagine activities, water does not move that fast. It does take a long, long time. So if your recharge area is one kilometer and you're one meter at least, let's start with a meter. Okay, so your recharge area is one meter. You have a recharge dam or something. And then water fills in and then it comes to the clay layer. For it to come to your point, which is one meter difference, how many years does it take? Given that it moves only 0.3, 0.3 millimeters per year. Okay, so do the calculations. How many millimeters are there in a meter? Do that 10 power minus. Okay, so do those calculations and then get at how far this water is being transported. Okay, so it's approximately 10 power minus 3. Am I right? So you're not even getting at your meter within 10 years. So those estimates that I showed clearly in the previous lectures on how water moves, sometimes it became days. So like here, for example, it can come within a day, the water. That's why it can transverse 300 kilometers in a year. Okay, so let's divide it by 365 approximately. So one kilometer per day, the water can move in a gravel bed, one kilometer. But if you come to your centimeter analysis millimeters for your clay, it doesn't even move within 10 years. So this is the analogy you need to understand when you're doing the groundwater related recharge mechanisms, groundwater use also. So if someone is using too much groundwater in those regions, you need to tell them that this is not sustainable because you can pump it within a day. You can pump 10 liters, 20 liters within a minute. But how long does the water take to come to that point is the question. So you are actually depleting an aquifer or a storage, which has been sitting there for a long, long time. So you need to be very, very calculative about it. Moving on on to the variations of hydraulic conductivity, the multiple factors that contribute to the complexity of hydraulic conductivity. Let's look at some heterogeneity and anisotropy. Rocks are heterogeneous, which means inside your soil material, inside the rocks, you don't see the same size, same type sometimes. There's always a mixture. As I clearly said earlier, you don't find a pure one type of soil or a rock in a location. It is heterogeneous. Let's define heterogeneity and anisotropy. So let's take one example. This is your soil bed. I'm leaving the Y plane. So you have your Z plane and then your X plane. So there is another Y plane. I'm not looking at it because this is a 2D image. You're saying only Z and X direction. So there could be one Y direction this side, but we're not going to look at it. First sample. So I'm taking four samples and I'm going to explain what is heterogeneous isotropy and anisotropy in terms of hydraulic conductivity. So hydraulic conductivity is given as K. Sometimes I will write it as small K also, so don't get confused with permeability. Mostly only hydraulic conductivity is used for your modeling because permeability is a function within new hydraulic conductivity. So coming back, we do have a location. So this is a location in the soil sample I take and I look at your sample and analyze the hydraulic conductivity. I'm analyzing here. So two points in the soil. I'm taking a sample and what I see is it is the same. KX is the same as KX, the value. Let's say if it's 5 meters per second, it is also 5 meters per second here. So it is homogeneous, which means it is same and isotropic along the distance, along the planes, along the directions also, it is the same. Now let's take homogeneous anisotropic. So for example, what I mean isotropic is KX is equals to KZ. So here it will be 5 meters per second, 5 meters per second. That is isotropic. It is the same value in both the directions. Whereas homogeneous anisotropic is, you have it different in different directions. So KZ is shorter than KX. KZ is shorter than KX, but it is homogeneous. If you take two points in the same sample, it is the same value for KX and KZ. So your values are the same along the sample. So it is homogeneous. However, the XYZ planes may differ. So heterogeneous means if you take two samples in different points, your KX, KZ are different. So KZ in point one is not equal to KZ in point two. KX in point one is not equal to KX in point two. However, it is isotropic. Isotropic means KX is equal to KZ. So you can see KX is equal to KZ. So both are telling how. Same here, heterogeneous and isotropic. So two samples are two different locations and both KZ and KX are not the same. Also, if you go from one point to the other point, the KX one is not equal to KX two. Same KZ one is not equal to KZ two. So you do have totally different values when you take in a two different locations. Ideally, this one is the best. Or you can also go along with this one along if you have KX and KZ estimated. For example, if you're working in a field and you find it as homogeneous and isotropic, you only have to find K value in one direction and then you can apply it throughout the field. So that is the best case scenario, but it is not possible in a natural system. This is what was assumed in your Darcy's equation at all. So coming back to homogeneous anisotropy, this is also can be okay because it is at least one point I can take in the sample and assume everywhere it is the same. But the reality is this, it is very heterogeneous and anisotropic. So anisotropic direction is very, very dependent on where you take the sample, how you take the sample, etc. So it is a direction property anisotropy, whereas heterogeneous is a spatial property. So property that varies from one point to another. Therefore, there is a need. Now, as I said Darcy was solving in one dimension. So now they know that okay, it is not the same in all planes and need not be the same in all locations within your sample. So there is a lot of variations of hydraulic conductivity. Therefore, there is a need to solve Darcy's equation at different points and take into account directionality. Because your water flow is a directional, if you don't have direction, where will the water flow? It can flow anywhere it likes and then create storages, spools, etc. So it is always important to visualize groundwater as a 3D component along three planes. Most probably your X and Y plane are almost same. So which means isotropy could be there in a K X, K Y, but K X and K Z are not isotropic. Why? Because you have your also, there's another pull of gravity acting on it. Please understand that this is the real case scenario. And most cases are like this. However, you can get away with K X, K Y plane, but K X and K Z are not the same. And between locations, also it is not the same. So given like this, someone can ask me how many samples should I take? How many is it possible? It is not possible to take a lot, but at least you could average it out, average the differences out by taking some samples and having a clear understanding of how the hydrology behaves. So basically, if you dissect your aquifer or your ground profile, under the ground, the profile of the soil into different specific unique structures like layers, layers or structures, then you can assign a homogeneity and isotropy in that location. For example, I have four layers in my cake or my soil layer. The first layer can be this. The second layer can be this. Third, fourth, like that. Okay. And you can put one value for each. So now you've created a heterogeneity in the soil profile. And also you have introduced an isotropy by giving two different values for K X and K Z. Do not give the same values. And those can be estimated by your groundwater model. Classes are expressed in vector shorthand can be Q is equals to minus K hydraulic conductivity, which is Q is your groundwater velocity, minus K del H of gradient of H hydraulic gradient, as I explained in the previous class, which is a function of your difference in the head by difference or difference between the two wells. Expanding vector shorthand of some flow in one dimension, we have Q X. So you're putting the X notations in the equation in just one plane, X axis, you have minus K D H by DX. Now expanding the vector in two dimensions, slowly you see how the complexity comes creeps into the equation, you have Q X Q Z, which is equal to minus K X S, K X Z, K Z X, K Z Z, del H by del X, del H by del Z. So or you can expand it as this. So slowly you could see I'm just going to go through the first one Q X is equals minus K X X, del H by del X minus K X Z, D H by D Z. So you have your partial differentiations also. So slowly you have made the equation complex, but please remember we are not stopping at two dimensions. We have three dimensions. So it gets more crazy, the equation. Okay, so you need to solve all this to find a Q in each direction. And as I said, you can probably get away by saying Q X is equals to Q Y, so you don't have to do this, but still the Z component in the different directions has to be accounted for. So eventually you'll be solving this. And since it is not solvable that easily through hand, it takes a long time, and you have to take a lot of assumptions, sometimes the models help. So when we go through the final stages of this course, I would go through an introduction of the modeling software. And just so that one should not ask, why are we learning models when we can do this through hand or manual calculations? It is important to understand, it doesn't take a long time and error prone. So if you do it by manually, sometimes you will be missing the connection between the dots. So it is always true. For example, you have to take one well and another will find the Q, then go to another well and another well. So think about how many wells you need to put in your visual imagery, and then estimate Q X along the way. So it does take a long time. So please understand that part. So hydraulic conductivity and permeability are tensors. Okay, how do we evaluate the component KIG of these tensors by solving them? So as I said, you need to solve them in a very unique and very careful way to account for the variabilities in hydraulic conductivity across the planes KX, KY, KZ. And for that, each K value has to be important. So you need KXX is here, KXY is maybe somewhere here. So you need to understand that the variabilities of the hydraulic conductivity plays a role in this and it is a three dimensional property. So all this solving and modeling is part of the advanced groundwater modeling course. But as I said, I'll just give an intro on why you need models, how to self-learn models in the classes to come. Some of these models are free open source. We would be only promoting open source so that everyone can access it. And the beauty about open source software is a lot of people have access to it and a lot of people contribute to the material, which means like if you have a section of this material and I'm working on it, for example, I can go in the forum or a group, a Google group or something and post comments on how to solve it differently. If someone has a problem, they can put it on the group and we can discuss it. So all this can be done in an open source software. Moving on, let me recap this wonderful week of groundwater hydrology discussion. And then we would wrap today's lecture. So groundwater hydrology components, we looked into the past week, all the four or five lectures we looked into specific groundwater hydrology components, namely specific yield, which is your trainable porosity, specific retention, which is how much water the soil can retain after gravity can act and pull the water out, which is more important for your plant life. We looked at porosity, which is a combination of specific yield and specific retention. And your porosity is nothing but the volume of voids to the volume of total solid. The volume of voids is a very important parameter in your soil profile for groundwater because that is where groundwater can be stored. And once the porosity is being connected between each other, then water flow can occur. If you have a groundwater soil component where water can enter, but it doesn't get connected between the poles, then what happens? It just gets stagnated, like a purged aquifer. So that also we would be not looking at here. We have the purged aquifer. So we would be not looking at it in detail. We did not look at it in detail because the presence of such aquifers is very limited. So most of it is connected. There's some connection so that groundwater flow can happen. So the components are different. You have groundwater recharge, groundwater discharge, groundwater flow. And for the flow, you need to have the connections. So that is one thing. Then we looked at groundwater recharge and discharge. We looked at spatiotemporal variations in groundwater recharge, spatial as layers between. So for example, the top layer or the confined layer can recharge from some days to some years, this part, some days to some years, depending on the type of soil material because the soil hydraulic conductivity is a varying factor. Then we looked at confined aquifers and the recharge time goes anywhere from years to millennium. So it is very important to understand that just putting, you can easily put a well and take the water out, but you need to understand how long the water takes to recharge. Then we moved on. We looked at these factors and how they're connected. We also looked at permeability and hydraulic conductivity. Permeability is the factor of the soil that allows, permits the water to come. And it is a function of the connection between the pores. We also looked at pore velocity, effective porosity, those kinds of concepts. We also then looked into the variations of them, the units of Darcy's, etc. Why were they varying? It's because of the nature of the soil profile and the nature of the fluid. Then we moved to hydraulic conductivity, which is one of the most important parameters. And we saw that it was a function of your pore properties and also your fluid properties. You can interchange permeability and hydraulic conductivity through these constants. We also saw that hydraulic conductivity is not granted to be the same across areas. There is a special difference because it is heterogeneous and anisopropic, which means it is not the same in multiple places that you take. The hydraulic conductivity can differ and within the same location, it is not the same in all the planes X, Y and Z. So understanding this is very important because your groundwater pump is Z direction. It just pulls it out, but water doesn't go that way. So when you do engineering and bypass these processes, it takes a long time for the water to recharge because it follows the laws of physics. It has to go through gravity. It has to go through the Z profile, then spread out when there's an impervious layer, these kind of things. Then we moved on to hydraulic conductivity three dimensions and the complexity of it because we know the variations after. So then we looked at the three dimensional aspect and how complex it is to solve these equations, which guarantees that it would take long time for you to manually and some errors can creep in. So it is always good to use a model. Then we also looked at water levels and hydraulic head. How is a water level defined? How is a hydraulic head defined and potential defined? All these we looked at given an example of a ground surface well and from the datum, we defined a datum as zero and from the zero level, how far is your profile? We looked at these different concepts to understand one value is if you know these components for hydraulic conductivity, porosity, specific yield for ground water, you know how it flows. So once it flows into your wells, now all you have is your water level. And from your water level, how do you understand ground water flow, which is your Darcy's equation. So we also looked at Darcy's equation, which was giving a flow and a velocity and it was showing that it was in a negative direction of reducing head because it flows from high potential to low potential, high head to low head water. So all these things we covered so that now we are ready to understand taking a soil from the field or a rock profile. We understand what would be the porosity. We visualized it as porosity, specific yield, etc. And depending on that, we know how much water can come in, recharge. And once the recharge comes in and stays as a water level, we know how to estimate from one water level to another water level, the flow, which is Q. Getting into your recharge, etc. activities, we will not be using models for that because recharge and discharge activities totally depend on land availability, funds availability, etc., which we will be covering in the future lectures. With that, I would like to conclude today's lecture. Thank you.