 In today's lecture, we are going to talk about runoff. Runoff is the component of precipitation which runs off from the catchment through the streams or other drains. We will start by looking at the hydrologic cycle with runoff components in details. So, let us look at the cycle once again. This is the ground surface. There may be drains, trees, there may be small depressions like lakes. So, when precipitation occurs, part of it will evaporate directly. Part of it will fall on the trees and other structures like roof of the buildings. From the roof of the buildings and the trees, some part will evaporate directly without reaching the ground and some part will fall down to the ground. Now, the part which falls on the ground, part of that will again evaporate from the ground surface. Part of it will go below the ground level and is known as infiltration. Now, once this water goes underground, there is below the ground a saturated soil layer and this is known as the ground water which moves very slowly. So, once the water reaches the ground water, it will move again toward the drain, but at a very slow rate. Some part of infiltration, if the soil is pervious and there is an impermeable layer, will go to the stream or will appear on the surface if the impermeable layer intersects the surface. This part is known as interflow. So, this is the part which infiltrates and then comes back again on the surface or in the stream. So, this interflow is also an important component. Now, the part of precipitation which does not evaporate or infiltrate runs on the land. This is known as the overland flow, overland flow. Part of this overland flow will go into the lakes and once the depressions and lakes these are filled, then the rest of it runs off to the stream. What we will look at today is this component. How much water runs off into the stream from a particular precipitation? Now, various components of the runoff, if we look at let us say a river cross-section and let us say the ground surface is like this and the ground water is here. The part which comes over the surface is known as surface runoff and the part which comes from the ground water is called base flow. The difference between these two is that surface runoff comes immediately or very soon after the precipitation while base flow for the same precipitation to appear in the stream as base flow it will take a long time because it will infiltrate into the water into the ground, reach the ground water and then it moves very slowly. This may take a few months or sometimes even years to reach the stream. So, there is a fast component and there is a slow component and we can write down various components in two forms direct runoff and base flow depending on how fast or how slow they reach the stream. In the direct runoff we can again have various components for example, surface runoff which comes over the surface. There is some rainfall which occurs directly on the stream surface. So, precipitation on stream and there is some part of inter flow which comes very fast back to the stream and we can call this prompt inter flow or rapid inter flow. So, the component of inter flow which goes into the ground and then reappears in a short time is known as the rapid or prompt inter flow and that is also counted towards direct runoff. So, this component entire component direct runoff component is the one which occurs a little while after the precipitation. The base flow component can again have two different parts. One will be a delayed inter flow and one would be the base flow. So, the delayed inter flow is the component of inter flow which goes into the ground and appears on the surface again, but not very fast. It takes a while sometimes a few days and base flow is the component which comes from the ground water and typically it takes a few months or sometimes even years. So, we will look at various aspects of these components and see how we can predict or estimate the runoff with or for a given event of precipitation. So, let us look at a river which has its origin at some point and now let us call this area. Let us say that this point is a. So, this entire area is the one which contributes to the flow at the point a in the river. This area is known as the catchment area. So, this is the catchment of the river at the point a. What it means is that all the precipitation falling in this area will ultimately reach the point a and it will be taken out of this area through the stream at point a. So, this catchment area has its boundary which is known as a water divide or sometimes watershed. Sometimes the catchment area is also called watershed. So, the idea of this catchment area is that any precipitation falling anywhere in this area would go to the river and then will be carried out of this area or run off from this area through point a. Now, if we take another point b then naturally the catchment area of b would be larger and it may look like this. If we look at the elevation then suppose the ground is like this and this is the river section then any water precipitation falling on this side may come to the river and a precipitation falling on this side may go out of this area. So, this will be a water divide defining the catchment area. Now, how do we study the run off in a river? Typically what we do is plot what is known as a hydrograph which tells us how the flow in a river or a stream varies with time. The flow typically would be in meter cube per second. The time may be in hours, days or even months depending on what scale we are talking about and if you look at the flow let us say over the scale of a year we might say that this is January, February, March and so on. The flow in a river may be very small during the months of let us say the winter months and up to may be may, but when the monsoon comes the flow will increase and then again it will go down and then in January it will again become very small. So, this is the hydrograph of the stream and it is very important to know the hydrograph because it will tell us what is the maximum flow in the stream, what is the minimum flow in the stream and both these are very important because the maximum flow will affect the design of any flood control works. The minimum flow will affect the storage requirement or whatever water we can take out of the river on a consistent basis it will affect that. So, both these are very important what is the minimum flow, what is the maximum flow. If we look at typical streams there may be three different kinds of streams one which runs throughout the year perennial for which the hydrograph will look like this because it will run through the year and there is no part of the year where there is no flow in the river. So, in this all the time there is at least some flow in the river, but the other kind of streams intermittent and ephemeral they may not have flow during some part of the year. For example, the intermittent stream may have a hydrograph which would look like this. So, in part of the year there will be no flow and during most part of the year there would be some flow in the stream. Typically, what happens in these kind of streams is that the ground water level. So, in absence of a storm when there is no precipitation falling on the area ground water flow or the base flow is the one which sustains the flow in the stream. So, in a perennial stream the ground water level will be above the stream bed and therefore, it will contribute water towards the stream throughout the year, but in intermittent streams the ground water level sometimes may fall below the stream bed and there will be no flow in the stream, but again during monsoons the ground water level may rise and therefore, it will have a continuous period of 6, 7 months or so in which there will be always be flow. Contrasting behavior is observed in ephemeral streams in which there is almost zero flow in most part of the year and only there will be some isolated flows in response to storms. So, as and when there is rainfall there will be some flow in the river and when there is no rain there will be no flow. So, these kind of streams the pattern of streams is important to know in order to design a storage or a flood control measure. Now, the runoff process or this hydrograph shapes it may have a flat peak, it may have a very sharp peak, the time base may be small, the time base may be large this depends on a lot of factors. So, next we will see some of the factors which affect the shape of the hydrograph. We would start with a hydrograph which is of a smaller duration. So, it in response to some precipitation over the area and then we will go to the higher duration behavior for example, annual hydrograph. The hydrograph which is in response to a storm is typically called storm hydrograph or simply hydrograph. So, in this lecture we will just use hydrograph for the storm hydrographs. So, let us see how the storm hydrograph shape is affected by different factors. The factors which affect the shape depend on the basin or the catchment basin and catchment are used they are kind of synonymous. So, some basin or catchment properties affect the shape of the hydrograph. So, what we are now looking at is when rain occurs how the runoff changes. So, over certain area let us say this is the catchment area, river originating here and moving to the point A and now let us suppose that there is some rain over this entire area. We will assume that the rain is of uniform intensity. So, the rainfall which occurs its hydrograph can be plotted as intensity versus time and it may be let us say uniform intensity for certain duration D. Now, if this intensity is less than the evaporation and infiltration from the basin then there will be no runoff. So, first it has to satisfy the evaporation, the infiltration and also depending on the presence of lakes and other small depressions the depression is storage. So, some part of it will go into satisfying the initial abstraction and we have already seen this in the chapter on infiltration that we can define an infiltration index phi which is taken out of the rain and then the effective rainfall is reduced. This hydrograph is called E R H the effective rainfall hydrograph. So, our interest is in looking at for a given E R H what will be the runoff hydrograph or D R H direct runoff hydrograph because in a hydrograph there will be some component which will have base flow and that is not a direct result of the effective rainfall. Therefore, we must remove that component and then study what is the relation between effective rainfall and the direct runoff. So, if you look at this catchment the one important factor is known as the time of concentration. Now, this time of concentration typically denoted by T C is the maximum time it takes for a drop of water anywhere on the catchment to reach the outlet A. Now, if we look at this catchment area which let us say does not have any tributaries. So, there is just one main channel and there is no tributary to this channel then a water drop falling on this point will first move over the land and then join the stream. A water drop falling here may move here and then follow the stream typically the velocity in the stream is much higher than the velocity over land. So, what we say that over land flow typically moves at a smaller velocity compared to the stream flow. Therefore, a point which is further from the outlet A. So, this point which is distance y that is further from the point A it may reach A sooner than let us call this point B and C. So, a rain drop falling at B will first move over the land to the river and then it will follow the river to the point A. A rain drop falling at C will first have to travel over the land to this point on the stream and then move towards the point A in the stream. Now, since the stream velocity is very high the rain drop at B may reach A sooner than C. So, it is not a distance which affects the time of concentration, but it is how far it has to go over land and how far then it will have to go through a stream. So, there is a time maximum time in this case it may be a point somewhere here or here. So, it will have to cover a lot of area over land and then will reach the stream and move to the point A. So, time of concentration is an important parameter in the hydrographs. So, let us now look at these factors for example, the basin shape how the basin shape will affect the hydrograph. Let us look at two basins which have everything identical for example, same length of river same size, but the shapes of the catchment are different. So, in one of them the catchment is wider near the outlet and narrower as we go away and in one the catchment is narrow near the outlet and it is wider as we move away. If we look at the hydrograph considering everything to be the same except the basin shape in this one we would expect the peak to come sooner and if we look at the curve because most of the rain occurring near the outlet point will reach very fast at A and also since this area is large the peak will be higher, but in the other case the hydrograph will be more flat because the rainfall which is occurring in this distant area would take some time to reach the point A. So, the shape of the hydrograph will be affected by the shape of the basin. The next factor may be the basin size. Size of course, decides the volume of rain occurring over the catchment. So, if the size is more the volume of rain will be more and therefore, typically the runoff will be higher. So, if you have a smaller size catchment the hydrograph may look like this for a bigger size catchment the hydrograph may look like this for the same rain because the same rain now is occurring over a larger area. So, it will contribute more volume to the runoff. Typically the peak flow is proportional to the basin area to some power n and n will vary from area to area. There are some typical values given in various books for different areas in India and outside India. The next factor we would look at is basin slope. Now, basin slope will affect the time of over land flow. So, if there is a channel and the catchment area the time it takes for rain to or a drop of water from to travel from B to C will be dependent on the slope of the basin. Higher the slope the smaller will be the time taken in travelling from B to C. Therefore, the base of the hydrograph the time base of the hydrograph will depend on the basin slope. Typically larger slope will have a smaller T B. Similarly, the stream slope also is important because the stream slope decides the stream velocity. So, higher slope again means higher velocity and therefore, it will affect the falling part of the hydrograph. This part which is typically known as falling limb or recession limb. This denotes the water coming from the storage. It may be channel storage or it may be storage inside lakes or small depressions in the area. So, this part will depend on what is the stream slope. If the stream slope is large this part will be showing a rapid decline. If the stream slope is small it will slow a flat decline. The next factor is land use for the same rainfall. If the land is open the soil is porous then most of the water will go inside the ground lot of infiltration and runoff will be smaller. But if the land is let us say paved. So, we have lot of roads parking lots and other paved areas then there will be less infiltration and more runoff. Similarly, vegetation also affects the runoff. If there is more vegetation there will be more interception there will be more transpiration and also the over land flow velocity will be reduced. So, if there is more vegetation typically the runoff volume will be smaller. Drainage density is another important parameter which affects the hydrograph. By drainage density we mean in the catchment area what is the length of channel and again this is channel network which includes all the tributaries also. So, if we have a tributary joining in here tributary joining in here and these tributaries may themselves have some smaller channels joining them. So, this is the length of the entire channel network per unit area of the catchment. So, divide by area of catchment this is known as the drainage density. So, this should also be the straight forward to look at if we look at two hydrographs with different drainage density for example, this may correspond to a network which has a smaller drainage density and this may correspond to a network which has a larger drainage density. Now, a smaller drainage density means that most of the flow will be over land flow and higher density means that most of the flow will be through the streams. So, it will reach the point a faster and the peak also would be affected by the drainage density in the area. Now, the flow here when the rain occurs initially there will be some flow because of the base flow component. So, if we want to study the effect of the rain we must separate out the base flow and the direct runoff. So, let us look at a typical hydrograph and see how we can distinguish these components and separate various components. So, if you look at this typical hydrograph the rain has started and it is conventional to show the rain on the hydrograph itself. So, the rain hydrograph is shown on the hydrograph itself to tell that this hydrograph is because of this rain. Now, if you see from this figure the flow in the river is decreasing even after a starting of rainfall. So, initially the flow in the river is base flow the base flow will be decreasing with time because as water is taken from the groundwater depending on the surrounding area its conductivity the water level will be going down and therefore, the flow in the channel will be reducing. Now, once the rain occurs the stream flow does not immediately start to increase because initially some part of the rain will be going into satisfying the evaporation and infiltration requirements. After a while so, we call let us say this point A at point A the rainfall has satisfied the initial abstraction and now the runoff has started. So, we call this A as the start of the direct runoff and then it will start increasing reach the peak. So, this point is known as the peak point q p. Now, at q p we have reached a maximum flow and this will depend on the time of concentration. Suppose our rainfall is more than the time of concentration in that case after reaching q p it might continue at q p for some time and then come down. But, typically the rain falls are not for that long duration because time of concentration is typically quite high and rainfall generally are for a shorter duration. So, once it reaches q p it will not continue at that level, but it will fall down. Now, on the rising limb this portion of the curve is called rising limb or sometimes even concentration curve. If you look at this part it is concave upwards at this point A and at the peak it is convex upwards. So, somewhere in the middle there is a point of inflection where the nature of the curve changes from concave to convex. Let us call this point of inflection as point B. Similarly, when the rain has just stopped and the flow is now reducing on the falling limb which is also known as recession curve because now water is receding recession curve. So, on the falling limb again the nature of the curve is changing from convex upwards to concave upwards and there will be another point of inflection here where before that the curve is convex upwards and after that is concave upwards. The portion from B to C encloses the peak. So, this B C is typically called the crest segment. So, A B is the rising limb, B C is the crest segment and then from C to a point D. The point D typically will be a point where the flow will be. So, after D we will have only base flow and there is no direct runoff beyond the point D. The direct runoff hydrograph would be if we very simply one method of separating the base flow is we join A and D. So, the curve A B C D would be direct runoff hydrograph D R H and also it is conventional to show not the total rainfall here. So, instead of showing the total rainfall we would show only the effective rainfall and the effective rainfall would look like this. So, effectively the rainfall starts at the point A because before that we say that whatever rain has occurred is not going as runoff it is satisfying the infiltration and evaporation requirement of the basin and if there is some depression storage. It will satisfy the initial abstraction requirements from the point A the effective rain starts stops somewhere and the peak will occur after the stoppage of the rain. Because when the rain stops the areas which are remote from the point A it would take some time for that water to reach the point A and therefore, the runoff will continue to increase even after a stoppage of rain. So, let us now look at the some of the methods which are used to separate the base flow. So, this is the effective rainfall point A is easy to spot because point A is the point from which the hydrograph starts rising that means the rainfall has started contributing. So, let us see how to spot various points on this we have already seen that point A it is very easy because this is the point at which the hydrograph is starting to rise B and C we do not need but I will just mark here these are the points of inflection which denote change from concave to convex or in other words the slope of this curve d q by d t will reach a maximum here if you look at the slope of this curve at the point A it would be 0 at the peak also the slope of this curve is 0 in between the slope is increasing it will reach a maximum at point B and then it will start to decrease and become 0 at the peak point C also we do not need for base flow separation, but I will show it here and the point D here is the one where we say that direct runoff has ended and beyond that we have only base flow. So, before this we have base flow and beyond D also we have base flow the region from C to D is recession which denotes the falling or decrease in the flow with time. Now, this part C to D is not affected by storm characteristics because storm has already stopped C to D is denotes the decrease in channel storage or some other small depressions which may be draining now after this rainfall has stopped. So, this will this recession limb is generally affected by three different parameters and what we say is that q during recession is typically given by a power law q 0 k r to the power t where k r is dependent on three different kinds of factors k r s k r i and k r b which are for the surface stream, inter flow and base flow, surface inter flow base flow. So, these factors k denote how fast the stream or the surface stream will decay the discharge from the surface stream will decay, how fast the inter flow is decaying and how fast the base flow is decaying. In most of the basins inter flow component may not be very large and typically k r i can be taken as 1 k r s denotes how fast the water is coming out of storage from the channel and as we have seen earlier it depends on the channel slope. If channel slope is large water will come out of it faster and base flow it depends on how the ground water contribution is decreasing. There are some typical values which are generally used for these coefficients. So, k r s is typically taken as 0.1 and k r b is typically taken as 0.9. So, this decreases very slowly this decreases at a quite fast rate. So, this tells you about the recession limb point D is the point at which we say that the direct runoff has ended and base flow has started. Typically, whatever is the base flow at the start of the hydrograph we can use a similar pattern here or we can plot this curve on a log or semi log scale and see where the curve departs from this equation q 0 k r t. So, we will look at some methods which do the base flow separation. The easiest method is to join A and D with a straight line. So, if this is the hydrograph we say that the base flow is given by this line joining A and D and whatever area is above this line gives the direct runoff ordinate at that time and then we can plot this direct runoff hydrograph separately which will have a peak equal to this value and a time base which is equal to A D. Time base of course, will remain same for all the methods because the points A and D we have already fixed. So, this method which is known as the straight line method is the simplest but there are some drawbacks to this method. One is some people say that the base flow does not remain constant throughout this period. Once the storm occurs the ground water level will also go up and the base flow should increase. So, there is there are different methods which can be used to improve on this. One of the methods which has been used is extending the curve on the rising limb or before the rising limb. So, if we have this point A and D and this is the time of the peak let us call this T p. Then we assume that the base flow will continue to decrease beyond A till the peak of the hydrograph is reached. Let us call this point C. C we have already used. So, let us call this point E and join E and D. So, A E D will represent the base flow contribution and then whatever ordinate is above this we take that as direct runoff. So, you can see that compared to the previous straight line method which used to join A and D. This method typically gives a higher peak. So, in this what we have done is extension of base flow forward from A. So, this is method 2 in which we extend of base flow forward. So, from A we have extended it till the peak and then joined E and D with a straight line. The third method is the one in which we extend the base flow backwards from D. So, again let us draw the hydrograph find out the points A and D. These are the D and C are the points of inflection. So, what we do in this method we extend extension of base flow backward from D. So, we extend the base flow component. So, this is going at a curve like this. So, we extend it till we reach the point of inflection and then we use another smooth curve to join let us call this point F. So, A F D will now give the base flow component and the peak in this case turns out to be smaller and these are the direct runoff components at various points. So, these are the methods which can separate the base flow from the total runoff in order to give us the direct runoff hydrograph or DRH. So, the DRH will start from 0 because the base flow is separated will reach a peak and will again come back to 0 because again the base flow is separated. So, there is only direct runoff component up to this point beyond this we have base flow in the river, but we are not showing it and the corresponding hydrograph can be shown like this. So, this is a very simple description of the hydrograph for a uniform rain occurring over the catchment. If the rain is not uniform sometimes the hydrograph may look like this. In that case the hydrograph may have a very different shape it may go like this. So, for a complex storm in which various intensities of rain occur for different times the shape of the hydrograph will be very different, but if we assume there are two assumptions if we make them then it makes the analysis much easier and those assumptions are called time invariance and linearity. In general rainfall runoff relationship is very complex if we have two different catchments the same rainfall will cause two different or very different hydrographs or for the same catchment if we have two different kinds of rainfalls they will also cause very different hydrographs. Sometimes even for the same catchment and same rainfall we may get different hydrographs it depends on what are they starting initial conditions. For example, if the soil is very dry rainfall occurs lot of it will go into infiltration and runoff will be smaller. For the same rainfall if the soil is wet initially for example, there is rain before that day soil will be wet. So, if the soil is wet there will be more runoff. So, not even the catchment to catchment, but even from event to event one rainfall to other rainfall event the hydrograph will be different. So, it is very difficult to theoretically analyze this unless we make some assumptions. So, these two assumptions time invariance and linearity help us in analyze the hydrograph and to estimate what would be the runoff for a very complex rain. So, time invariance means that with time the hydrographs are not changed if the same rainfall occurring no matter whether it is occurring at time t equal to 0 like this or if it is occurring at time let say t equal to 3 days it will produce identical hydrograph of course, it has to be shifted. So, let us look at t versus q. So, if there is a rain occurring here and generating a hydrograph direct runoff hydrograph like this and suppose we have another rain occurring let say starting from this point same intensity same duration then the hydrograph for the second rainfall event second storm would be exactly same as the first one only the base will be shifted like this. So, these two hydrographs this and this they will be same if the effective rainfall hydrographs E R H is same. So, that is the principle of time invariance that no matter where in time the effective rainfall occurs it will produce an identical hydrograph. The second principle which we have is the principle of linearity which says that if some E R H causes a D R H. So, this D R H direct runoff hydrograph is for this effective rainfall hydrograph then if the same duration rain occurs with a larger intensity. Suppose this intensity I 1 and there is another one let say with intensity 2 I 1. So, the principle of linearity says that the hydrograph the direct runoff hydrograph because of the second rain with intensity 2 I 1 the ordinate of that hydrograph will be exactly twice the ordinate of the first one. So, everywhere if you take the ordinate this ordinate will be twice this ordinate if the rain fall intensity is twice. So, the principle of linearity and time invariance they help us in analyzing lot of different kinds of storm patterns in order to arrive at corresponding D R H. And one of the most important theories which is used is known as the unit hydrograph theory. So, this unit hydrograph theory it creates a hydrograph for a unit rainfall and then using the principles of time invariance and linearity it tries to estimate for any other kind of rainfall pattern what would be the direct runoff hydrograph. So, before we discuss unit hydrograph let us look at D R H and look at the area under this curve because this will help us in finding out or deriving the unit hydrograph. This q is in meter cube per second and T is let us say in hours. So, area of this curve would give us some volume V if we take both of them in same units like meter cube per second and seconds then the area will come out to be in meter cube. If they are in different units meter cube per second and hours then we have to accordingly multiply it with constant to get the volume in meter cube. So, this volume would be let us say we have obtained this volume in meter cube. So, what does this volume indicate? This D R H is because of some E R H which has intensity i and duration and what we have said earlier is that this rainfall thus E R H is occurring uniformly over the entire catchment area. So, if the catchment area is A and the rainfall intensity is i duration is D. So, i into D will give us suppose this i is in millimeter per hour and D is in hours. So, i into D will give us amount of rain in millimeter units. Now, this is occurring uniformly over the whole catchment area. So, if we multiply A into i into D we would get a volume and since this D R H is a result of this E R H these two volume should be same. So, this i into D is the amount of rain which is falling in terms of depth. This is the depth of rain falling over the whole catchment area and this will be different for different duration and different intensity. So, when we talk about unit hydrograph we say that we normalize the depth of rain to a unit quantity. So, the depth of rain should be a unit let us call it depth of precipitation. The unit which is used typically in India is 1 centimeter. In some countries depth of precipitation is taken as 1 inch for the unit hydrograph, but we will take 1 centimeter as the unit rainfall. So, what it means is that if we have 1 centimeter of depth falling over the catchment in let us say D hours then the direct runoff hydrograph which results from that rain will be called a unit hydrograph for D hours. So, let us take an example D Q and let say we have a rain falling for 3 hours then its intensity must be 1 over 3 centimeter per hour. So that the effective rainfall total depth is 1 centimeter. Now, because of this E R H whatever D R H will get would be called a unit hydrograph and since duration is very important 3 hours we call it a 3 hour unit hydrograph. Similarly, if we have a rain which is falling for 2 hours intensity will be 1 by 2 centimeter per hour and the resulting hydrograph would be call a 2 hour unit hydrograph. The area under the unit hydrograph represents a the catchment area into 1 centimeter.