 Welcome to lecture number 40 of ground water hydrology course. Today, we will talk about this modeling and management of ground water. Under this, the topic that we will cover in this particular lecture is ground water-surface water interaction. In lecture 39, we have talked about this conjunctive subsurface modeling with surface water for overland flow case and we have already talked about this Vados zone flow thing. In this particular lecture, we will talk about ground water-surface water interaction. Let us consider one shallow aquifer ground surface and then we have one stream there. This is the direction of flow for the stream. So, flow and let us say that this is our water table and this is the stage height in your stream and this is the water level in the nearby aquifer which is again shallow aquifer or unconfined aquifer. In this case, there will be flow from your ground water table towards the stream and the aquifer will contribute some amount of water in stream. So, again we have unsaturated zone here and this is basically top cover. So, grass cover or any other kind of cover is there on both the sides. So, this is the situation where our aquifer is contributing in the stream. So, we can say that this is basically gaining stream. That means, stream is gaining from our aquifer. Now, if we see the water table contour for this particular aquifer, then it will be some kind of interesting thing because there will be deviation of water table contour if there is a stream in between a particular aquifer region. So, let us say that this is my whole domain. Now, I have contour of different hydraulic head level. So, let us say this is level 70, 60, this is 50. Now, we have a stream here which is starting from this point. Now, if you have that contour near to this stream, there will be some deviation. So, this is corresponding to 30, this is corresponding to 20 level. Now, if we draw one arbitrary line here. So, we will see that in aquifer region, your groundwater table is not deviating. This is groundwater flow line which will be perpendicular to this. So, this is basically groundwater flow line and these are water table contours. So, in this case, let us say we have two points A and B. So, starting from A, if we move towards this stream, then we will find that there is deviation and this contour is pointing towards the upstream direction. So, in line cross section, the water table is at a lower elevation at the interest section point and in this case, we can say that our groundwater contours will point upstream in a gaining stream. Similarly, if we see the thing for losing stream where things are similar, but only difference is the water level in aquifer and stream. So, this is our ground surface. This is the water level and water table in the aquifer is lower than the aquifer level of water in the stream. So, this is our water table. There will be movement of water from stream towards the aquifer. So, we can say that this is our losing stream. Like gaining stream, if we draw the contour levels, we will see the opposite thing compared to our gaining stream. So, let us say this is our stream direction and this is our contour level. We have this 190, 80, 70 water table contours. So, in this case, if we draw straight line as we have drawn it for gaining stream, we will find that this contour will point towards the downstream direction and that is at the intersection point with the stream. So, we can say that in this case, our ground water flow is like this which is away from our stream flow direction. This is ground water flow line. So, in this case, we can say that if the contour point downstream, the contour point downstream, so this is losing stream. So, difference between losing and gaining stream is that the ground water flow line in case of our gaining stream was towards the stream, but in case of our this losing stream, this is away from the stream. So, another special case of losing stream may be there which is some kind of extreme situation for the stream aquifer interaction. So, in this case, this is the flow direction. We have again that shallow water aquifer and water table is below the bed level of the stream. So, in this case, water table is below, so there will be contribution of flow from our stream and this kind of situation will be there due to excessive pumping in aquifer region. So, this is basically disconnected stream. So, in disconnected streams, we have ground water table which is below the stream this is our stream and this is our stream bed level. So, this is always below the stream bed level. So, these are called as disconnected streams. Now, we need to see what kind of fluid dynamics is there near to stream and that is in our aquifer part. So, in this one, if we draw one arbitrary cross section. So, in this one, we can divide this whole region, this is near to stream, this is pointing towards stream and this is towards our land. Now, if you divide this the whole thing into 3 regions that is A, B, C. So, in this region, the behavior of the total head is different. Let us first draw the water table for this cross section. So, near to this land, there will be sharp change in the contours. Let us say this is 120, this is 110 and this is near to that 60, again some 70, 80, this is 90, then 100. So, in this region, there is vertical flow, almost vertical flow in this part of the cross section. This is zone C or we can say this as zone. So, next part there will be almost vertical contours. So, these are 40, 30 and from there, let us say again there is change in the pattern and now in this region A, things are not that vertical. There is again curve kind of contours which will be available. So, in region B, there will be horizontal movement of water and in this region, there will be movement of water in upward direction. Now, if we install piezometers in these 3 different regions, then we will see what is the difference in hydraulic head that we will observe. So, let us say that we are installing piezometric heads here, then it will correspond to the water level here, then if you are installing piezometers here. So, it will exactly level with the water table and if we further go down, then there will be again lowering of the piezometric level. So, let us say this are region C prime. So, with zone C, this C prime is nested monitoring locations and in this nested monitoring locations, we can see that for a monitoring well in this region, there will be equivalent water surface which will correspond to this level. Again for monitoring well in this region, there will be equivalent water surface which will be corresponding to this level and this is at the top surface. So, this will correspond to our original water level, but interesting part is that almost in 2 cases, we have found that for a particular region or piezometric head is lower than the water table at that location. In this case, if we try to draw the thing, then we will see that this is almost static even if we go down, there will not be that much change in the water level in the piezometers. So, this is almost same because vertically there is no variation in contours. In this region that is region A, so this thing we can denote it as B prime. Now in C prime region or else we can denote it with piezometers with this red thing. So, in this region A, let us say that we have one nested network of A prime. So, if we install piezometers here, what we will observe? Observation is that or water surface or piezometric head will be above water table. So, we can say that there will be in first case, this is lower than our water table. This is almost similar to water table, there is not much deviation, but in this case it is higher. So, if we can install piezometers here, so there will be spontaneous water flow from these piezometers. And if we have deep wells in topographic depressions particularly in river valleys, then the water will spontaneously come out and that is which is known as artesian wells. And when water is discharged naturally to the surface and discharge point is called as springs. So, artesian wells, if we install wells and the water comes out spontaneously, then we say that this is the artesian well. And if the water comes out naturally to the surface, then we say that these are springs. Another most important point that is bank storage. What is the effect of bank storage on groundwater surface water interaction? Bank storage effect. So, if we draw it, you will see that with our shallow groundwater aquifer, these are our ground surface. In this case water level which is this and interestingly this is our water table during base flow. So, points A and B are there. So, what is this bank storage? We have flow direction, we have high stage here. Bank storage occurs when the water level elevation in a surface water body increase beyond the groundwater elevation in the adjacent. So, we have flow direction, then we have high stage. So, there will be movement of water in this direction. Through banks, there will be movement of water towards the aquifer. So, this is called as bank storage. This is water table at high stage. Interestingly, there will be movement of water from bank from stream towards this banks and there will be elevation of water table and after sometime when it reaches when the balance equilibrium reaches in the system, there will be higher water table near to stream compared to this lower ground water table during base flow. And in that equilibrium condition still beyond this point A and B, there will be movement of water from these beyond these two points in this direction. This is very complex in nature and water near the stream in that case water near the stream moves towards the stream, but it is beyond this A and B points which are intersection points during high stage levels in streams, there will be movement of water towards the aquifer. So, these are the direction of water flow situation. So, if you want to model this thing in practical situation, then we need to idealize this particular system with some simplified assumptions. Now, let us see that we have some aquifer and in that one we have some rectangular stream channel. So, in that rectangular stream channel, let us say this is ground water level and there is one region near to this channel that is riverbed sediment on both the sides and let us say this is our water level. So, with respect to our datum which is below this system, let us say this is our x coordinate system, this is y coordinate system and this is in the direction of that stream this is l and the saturated thickness in this one is taken as m h m and water table from predefined datum is h and z 0, this is elevation of the stream bed level from the datum and this is width of the channel B and this is height of water in the channel and we have thickness del z prime is the thickness of bottom sediment along the weighted perimeter of the channel. So, with this configuration we can write our governing equation for stream flow we can write the equations as z del v by del l plus v del z by del l plus del z by del t equals to q l and q v divided by B. So, here q v is the flow into the channel per unit width per unit length through its weighted perimeter and q l is the lateral inflow per unit length over the channel banks and from tributaries and again we need to have the momentum equation. So, this S naught is the bed slope and S f is the friction slope. So, this is for stream flow now we need to write the equation for ground water flow. So, ground water flow in unconfined aquifers will have a different thing. So, in that one dot t del h equals to S del h by del t plus q v B plus 2 z which is weighted perimeter of the channel. Now, this is valid for the lower part of the channel and governing equation for the other parts that will be k which is hydraulic conductivity this is H m this is saturated thickness of the aquifer H m then del h this is S y or specific yield. In this case this is storage coefficient and this is specific yield for the aquifer and there will be coupling between this equation this equation this one and this one that is continuity momentum for saturated confining portion and unconfined portion that will be coupled by Darcy's law and this is q v B 2 z this is Darcy and flux q v is the flow into the channel per unit length through its weighted perimeter. So, we can say that this is the Darcy and flux and Darcy and flux left hand side Darcy and flux right hand side we should have hydraulic conductivity and this is hydraulic gradient. What is hydraulic gradient here z plus z naught this is the total head for stream and we have head here that is H for any arbitrary location then we have this del z prime that is the difference between these two. So, we can say that this is our hydraulic gradient and it is a coupling our all the equations then to solve it we need certain boundary conditions. For open channel flow or river flow or stream flow we can either specify stage or discharge at upstream location and we need to specify stage discharge relationship for downstream location. So, this is for stream thing and for aquifers we will consider the whole region as impermeable. So, we have stream here which is flowing like this and this parts this is our x and this is our y axis. So, this is basically del H by del y this is 0 in this case this is del H by del x is 0 here also we have del H by del x equals to 0. So, we can choose a very large region and we can put that hydraulic head change to 0 that way we can manage the boundary conditions. The initial condition for stream flow are depth and velocities. So, depth and velocity that should be known for initial condition and with this configuration we can get the variation. So, variation will be like this where this is our upstream direction and this is our downstream portion. So, for any flood wave there will be change in the hydraulic head in the aquifer with the change in the peaks of flood wave. So, if we draw one simple figure maybe for some intermediate point here then we will see that if this is our hydraulic head then for flood hydrograph with no leakage this is positive direction this is negative and this is change in stream discharge from steady state flow condition. So, this is flood hydrograph this is without or no leakage. So, there will be change in the change in this let us consider this is with no leakage. So, it will merge here with leakage there will be reduction this green line and if we consider the effect of leakage then we will see this difference will plot it in this. So, this will be the same. So, this is basically the effect of leakage. So, the net effect of leakage or net effect of bank storage this is bank storage or we can say that effect of leakage is our bank storage. Now, we can have other situations where our pumping will influence pumping will influence the whole thing. So, let us say that we have region now this is our ground surface and this is our water table which is matching here this is confined bed water table. So, there will be flow from this direction towards the stream this is actually our stream and this is ground surface or land surface. So, there will be movement towards this stream. Now, if you place some well here interestingly with small amount of pumping there will be water divide and again there will be movement in this side also this side, but it will be in normal direction, but if you have some amount of heavy pumping then it will be directly connected with the it will be directly connected with the stream stage and we will see a different water drawdown in the pumping value this is pumping. So, these are the effects of aquifer on the stream and there is a reverse effect of stream on aquifers. So, amount of pumping also dictates the water divide. So, in the second case where we can have some amount of water divide for low pumping value, but for high pumping value this will be directly connected with the stream level. So, this aspect is important because our aquifers can directly influence the stream water level. So, there is always interaction between streams and aquifers. Most importantly if you have two reservoirs let us say that one reservoir is leaving water at certain rate another reservoir is leaving at a different rate. So, in between if there is too much extraction. So, in stream there will not be much water available. So, this is the total effect of stream water aquifer interaction this ends this lecture number 40.