 In the previous lecture we had seen abstractions from the precipitation and we also call it loss because we are interested in the surface runoff. So, whatever is not going to surface runoff would be called losses. We have looked at different kinds of losses or abstractions which are interception then we have depression storage, evaporation and transpiration and infiltration. The interception and depression storage they are combined and called initial loss and similarly evaporation and transpiration are combined called evapotranspiration or consumptive use. So, we looked at some of the processes what is the mechanism of these processes and today we will look at how to estimate these quantities. So, let us start with the estimation of the evaporation. As we have discussed evaporation is from a water surface transfer of water vapor into the air below the boiling point is known as the evaporation and as we have already seen that it is proportional to the rate of evaporation will be proportional to delta E which is the vapor pressure difference. This is the vapor pressure corresponding to water temperature and E A is the vapor pressure in the air. So, the difference of these two vapor pressures will drive the evaporation. There are lots of methods of estimating evaporation. We can directly measure the evaporation for example, we can put some vessel and then we can see how this water level is going down with time and that will give us some idea about the evaporation. We can correlate this evaporation with evaporation of a nearby water body. So, measurement is one method of estimating evaporation. We can also use some empirical equations. For example, we know that E is proportional to delta E. So, we can use some empirical equations like E equal to some constant k into delta E. Now, this constant may be a constant for a particular area or it may also depend on some other factors. For example, we have seen that the wind speed is important. So, k may be dependent on wind speed or we can have another function here which is a function of the wind speed sometimes atmospheric pressure and so on. So, these kind of empirical equations have been derived for various locations, but they would typically be valid only in that area. Universal acceptance of these empirical equations is not very common. Then we can apply some theoretical analysis and estimate the evaporation. So, today we will look at these techniques of measurement, empirical equations and some theoretical equations. Now, measurement of evaporation is quite straight forward that we put a pan. Let us say we want to estimate the evaporation from a lake. So, on the surrounding area or nearby this lake, we can put a pan and we measure the water level at different times. This will give us an idea about the depth of evaporation and then knowing the time, we can find out the rate of evaporation in let us say millimeter per hour or millimeter per day whichever units are convenient, we can use that. The evaporation pans sometimes also called evaporimeter because they measure the evaporation. One of the standard evaporation pans was used by US weather bureau and is known as glass A. The dimension of this pan, generally it is made of galvanized iron. Typically, the dimensions would be the diameter of 1210 millimeter. So, this is a circular pan, the diameter of 1210 millimeter, height of 255 millimeter. The water level typically is 50 millimeter below the top and this depth of water within the pan, we try to maintain it to 180 to 200 millimeter. So, we start with about 200 and then when the water level goes deeper at about 180, we again fill it up to make this level up to the original level below 50 meters from the top. The evaporation depth is measured and we call that pan evaporation E p. The lake evaporation or the evaporation from a nearby water body will not be equal to the pan evaporation and therefore, we write the lake evaporation as some fraction multiplied by the pan evaporation. C p is the pan coefficient and its value will depend on the type of pan which we use. For example, for a US weather bureau class A pan, C p value is generally around 0.7. This means that whatever evaporation we get from the pan, we have to multiply with 0.7 to get the lake evaporation, which implies that the pan evaporation is generally higher than the lake evaporation. And there are lots of reasons why pan evaporation is higher than the lake evaporation. First, if you have a pan and you have a nearby water body, the effect of size is important as we have seen that larger body will typically store a lot of heat. So, whatever radiation is coming in now this solar radiation is the driving force for the evaporation. So, whatever radiation is coming in some of it will get absorbed into the water body and will not cause evaporation, will not be available for evaporation. But for a small pan, radiation will be available for evaporation and therefore, the pan evaporation will be larger than lake evaporation. So, effect of the size or you can say heat storage within the body causes pan evaporation to be larger than the lake evaporation. So, E p will be larger than E l because of this storage capacity of the body. Then the pan is generally on the ground surface. So, there is a wooden frame on which this pan is kept. There is heat transfer from the sides also. So, there is some solar radiation occurring from the sides and also from the bottom. While in the lake which is ground surface is here, in the lake from the sides and the bottom, there is hardly any solar radiation coming in. Most of the radiation is coming from the surface. Therefore, again since more radiation is available in the pan, more heat energy will be available, E p will again be greater than E l. So, the sides and bottom will get some solar radiation and because of that, the heat energy available will be larger. So, larger body has more storage and therefore, less heat available for evaporation. Pan, the sides and bottom are open to atmosphere. So, they also get some solar radiation which will directly contribute to larger evaporation. Another reason that in a pan, there is rim above the water level and this will affect the wind action. While there is in a lake, whether the water level is here or here, the wind action will be almost same, but in the pan, the wind action will get affected by the presence of the rim and because of a smaller size also, a smaller wind velocity will be able to remove the saturated air from this. So, the critical wind velocity is smaller because the size is small. So, a smaller wind velocity will be able to carry the moisture from above the pan, but for a lake, a larger wind velocity is needed to remove the saturated air from above the water level. Therefore, for a wind velocity which is more than the critical wind velocity for the pan, but less than the critical wind velocity for the lake, the pan evaporation will be higher than the lake evaporation. And one more reason for pan evaporation being higher is that the pan material is different, typically more conductive. For example, galvanized and for class A pan and therefore, it will conduct more heat and evaporation will be larger. So, because of all these factors, size, the material, wind action, open to atmosphere, because of all these factors, the pan evaporation is higher and therefore, we need to use a coefficient of 0.7 for class A pan. In India, there is a different type of wind modification in this US weather bureau class A pan. It has been slightly modified and we use a pan which is known as the Indian standard pan or modified class A pan. So, the class A pan which was used by US weather bureau was slightly modified by the Indian standard institute. Dimensions are very similar. So, we have a dimension of instead of 1210, we use 1210 and 122. The height of water is measured by using a stilling well. So, there is a stilling well here which will damp out any fluctuations in the water level and the stilling well has a water gauge here, a fixed gauge to measure the water level. So, the water level will be measured on this gauge. There will be a thermometer also which will measure the temperature. So, there will be some temperature measuring device here. Again, this is also put on a wooden frame. So, there is a frame here and then wooden blocks perpendicular direction so that air circulates freely around the bottom. This pan has a coefficient C p of about 0.8 and the material the other modification which is done in class A pan that in we had used galvanized iron in class A pan, but in IS pan typically we use copper as the construction material. It is also painted white on the outside while class A pan is unpainted. So, there are minor differences in the size in the painting of the surface and in the material of the pan. Because of that the pan coefficient instead of 0.7 for class A pan, the modified class A pan has a coefficient of 0.8. There are other pans also other types of pans also which are used, but some of them are very expensive. For example, one of the major objections in using evaporation pan is that it is not representing the actual behavior of the lake. This is open to radiation from all sides while the lake is not. So, sometimes we use pans which are known as sunken pans put under ground. There is some part extending above ground and water level typically corresponds to the ground level and since this is sun the sides and the bottom they are not exposed to solar radiation. And therefore, this will be closer to the lake condition than the class A pan or the IS pan. The disadvantage is that it is very difficult to if there is a leak it is very difficult to find out the leak because in above surface pans it is very easy to see the leaks because it is all above the surface. But since this is sunken below ground if there is a leak we will not be able to know about it. And therefore, the estimate of evaporation which we get. So, water level is going down, but part of this may be because of the leak. So, we may over estimate the evaporation compared to the actual evaporation because of the leak. Also it is expensive because we have to dig and install it. So, these two factors because of its cost and because of inability to estimate the location of leak or presence of leak it is not typically used in India. The other types of pans which are used are known as floating pans. And they as the name suggests there are some floating drums on which these pans. So, floating drums on which the pans are put. And then we say that since these pans are floating in the lake they will represent the lake conditions quite accurately. Again the problem is that they are expensive. And the second problem is that measurement is quite cumbersome because since they are floating in the lake it is difficult for people to go in there and then take the reading. So, the reading is taking procedure is quite cumbersome and because of expense also they are not very commonly used. So, these pans are the common method for measuring the evaporation. If we cannot measure or suppose the evaporation pan is not available there is a requirement of density. So, pan density is suggested by world meteorological organization for arid area where we expect high evaporation. We should have one evaporation pan in an area of about 30,000 kilometer square. So, 30,000 square kilometer area should have one pan. But if we have cold areas where we do not expect very high evaporation then we can have a smaller density up to 100,000 square kilometer we can put one pan. And in between like humid areas which will be somewhere in the intermediate range we can have one pan in 50,000 kilometer square area. So, this area is quite large and evaporation pan may not be available near a water body for which we want to estimate the evaporation. So, under these cases we may have to go for some theoretical or empirical models. So, we will look at some empirical equations and as we have discussed they are of the form that evaporation is proportional to the change or difference in the vapor pressure. So, we write E L which is the lake evaporation, some constant K times there will be some function of wind velocity because we know that the wind velocity is an important parameter governing the evaporation and delta E which we can write as E w. So, most of the empirical equations they are based on a particular area in which the experiments have been conducted. E L has been measured, wind speed has been measured, the delta E has been measured and K has been obtained from that experiment. Two very common empirical equations which have been used, one is known as the Meyers equation which says that the value of K is around 0.36 for large and deep body and it is about 0.5 for shallow or small shallow. So, if the water body is large or deep you can use 0.36 otherwise 0.5. F u is a function of the wind velocity and in Meyers equation it has been given as u 9 over 16. Most of these equations were derived in the FPS units and therefore, this 16 term comes because instead of being in miles per hour we use the wind velocity 9 meter above ground. So, u 9 indicates that the wind velocity is measured at a distance of 9 meter from the ground. As we know the wind velocity typically shows a variation like this at the ground level it will be almost 0 and as we move up from the ground let us say at a height of h the wind velocity u h will typically be proportional to 1 7th power of h. This is known as the 1 7th power law in the boundary layer. So, u h is typically proportional to 1 7th power of the height. This 16 comes in the original equation this was 0.1 that means this was 10, but since we are converting miles per hour to kilometers per hour this factor of 16 also comes there. So, once we know whether what kind of water body it is we know the K we can measure the wind velocity. Wind velocity measurement is generally done at some particular elevation. So, this 9 meters or 30 feet was the commonly used elevation, but if we measure at some other height suppose h 1 we can always convert any other measurement. So, if we measure u 1 at h 1 we can always converted to u 9 by. So, u 9 over u h 1 would be equal to 9 over h 1 to the ground level. So, the power 1 by 7. So, by measuring u h 1 and h 1 we can obtain u 9 from this equation and use that in Meier's equation. The other two terms which we need are saturated vapor pressure and this is vapor pressure in air. The saturated vapor pressure E w is a function of temperature and typically a curve like temperature versus E w would be available to us. For example, T equal to 0 degrees 5 degrees 10 degrees 7 degree 8 E w is typically expressed in millimeters of mercury and its value may be 4 5 6. So, once this graph is available to us knowing the water temperature we can obtain the value of E w and E a would be relative humidity times saturated. Relative humidity measurement is typically done in weather stations. So, this will be known to us and knowing saturated vapor pressure we can estimate what is the E a and therefore, in Meier's equation we would have all the quantities available to us which will give us the lake evaporation. Another empirical equation which is common is known as the Rovers equation in which the atmospheric pressure has also been taken into account. So, P a is the atmospheric pressure into wind velocity factor is taken as 0.44 0.0733 U 0 and then you have delta E term. So, we will notice that we are using U 0 rather than U 9. So, in Meier's equation the velocity was measured at 9 meters above the ground surface this U 0 indicates the velocity should be at the ground surface at the ground level typically about 2 feet above the ground or 0.6 meter because immediately at the ground level no slip condition will say that the velocity should be 0. So, velocity at the ground level typically is taken 0.6 meter above the ground level. So, this we can measure or if we do not measure we measure some other height we can convert it using the 1 7th power law E w and E a we have already seen how to obtain P a is atmospheric pressure and again this P a is also expressed in millimeters of measurement of P a is also done regularly on weather stations. So, this gives us an estimate of the lake evaporation using empirical formula. So, empirical equations are good, but typically they are valid only in the area for which they have been derived and not universally. Therefore, we should look for some theoretical equations which we will now do the theoretical equations are generally based on some balance of some quantity. For example, water volume or heat energy or they will be based on turbulent boundary layer mass transfer. So, we will have 3 different kinds generally have been used the first one is based on the water budget the second one is based on energy budget and the third types of theoretical equations can be derived based on mass transfer through turbulent in water budget we look at a water body find out what is the inflow find out what is the outflow except evaporation. So, if we obtain everything other than evaporation then we can obtain by water balance what is the evaporation. So, that is the idea behind the water budget equations for estimating the evaporation. In energy budget we look at what is the energy which is coming. So, this was volume of water here we look at energy. So, what is the solar radiation on this body what is the solar radiation which is being let us say radiated back or reflected back what is how much is transferred to the ground to the air. And then we can say that the remaining portion will be used for evaporation and once we know how much energy is being used for evaporation we can find out what is the volume of water which is being evaporated. In the turbulent mass transfer we use the boundary layer theory. So, in the boundary layer the velocities are typically varying like this and there is a turbulent motion that means there will be fluctuations of velocities. So, if we look at the velocity at any point it is fluctuating with time. So, there is some mean velocity, but there are lot of fluctuations and these fluctuations cause a mass transfer from one layer to the other. And looking at the theoretical behavior of this mass transfer we can evaluate the concentration of water vapor in the water in the air and that gradient will be affected or the gradient and the fluctuations will cause the mass transfer or will cause evaporation. These theories are little more advance. So, we will not look at them here. Only these two water budget and energy budget we will look at here. In the water budget typically we take a time period of sometimes a day or a week or a month typically a day. So, what is the amount of water coming in and going out in a day and using the water budget we can write an equation like this. So, the slake evaporation or evaporation from the water body can be related to the precipitation v s i and o. These are the volume inflow and outflow from the surface water. So, surface flow in and out the subscript i represents in and o represents out s means surface. So, volume of water which is coming through surface flow in and out that will give you net inflow. Similarly, this is ground water again in and out. So, this term gives the net ground water inflow into the lake. T l is transpiration loss. Typically it is very small for a lake, but just to be more accurate we consider T l also and delta s is a change in storage. So, what water budget tells us that if we know the amount of rain falling on the lake, if we know what is the net inflow through surface water, what is the net inflow through ground water, what is the transpiration loss and what is the change in storage. We can find out the evaporation from the lake, because that will be the net result of all the other processes. Precipitation is easy to measure and surface inflow and outflow they are also comparatively easier to measure, but the component which includes ground water flow inflow and outflow is not so easy to measure. Transpiration loss is also not easy, but sometimes since it is very small, most of the times we can ignore it. Delta s is easier to measure. So, ground water flow is a very uncertain parameter. Measurement of this ground water inflow and outflow is not very accurate. That is why this water budget may not be able to give very accurate results for the lake evaporation. And therefore, we can go for an energy budget approach in which we look at the total energy coming to the body and amount which is lost and therefore, the remaining is used for evaporation. So, if we look at various components, we can write the heat energy which is used for evaporation as h n minus h a minus h g minus h s minus h i. This is the heat energy used for evaporation. So, all of these h are energy which is really heat energy. H e represents the heat energy used in evaporation. H n is the net heat energy which is received by the water body or the lake. H a is the net heat energy which is the heat which is transferred to air or lost to air. So, we can say that this is the heat transferred from water to air or we can say sensible heat transfer from water to air. This is heat transferred to ground. So, after total heat energy received by the body part of it is transferred to air. Part of it goes to ground. The two other losses are heat transfers. One is storage. So, there is some heat out of the total net radiation. Some of the heat will be stored in the water body and then there is some part which is advected through water. So, the energy budget relates the energies which are used for different purposes. H e as we have seen is for evaporation. H n is the net energy received. H a transferred to air. H g transferred to ground. H s stored in the water body and H i is advected through water. So, what it means is there is some water which may be going out of the water body and that will carry some heat energy. That will be the advected heat energy through water and it goes out of the water body and therefore, has to be accounted for in the energy budget. So, if we know all the quantities other than H e, we can obtain the value of H e and the amount of heat energy used for evaporation can be used to obtain the lake evaporation. So, if we know the H e value then it will depend on how much lake evaporation we have. So, if we know the mass density of water which is typically known. So, mass density latent heat of evaporation and this is the lake evaporation as we have discussed. So, if we know the heat energy used for evaporation knowing the mass density and the latent heat we can find out the lake evaporation. So, let us look at some other terms and see how we can obtain them. So, let us rewrite the equation net radiation coming in, loss to air to the ground, storage and advected out. The net radiation coming in will depend on what is the total radiation coming in and what is the reflected back radiation. So, we can write this as H c into 1 minus r. Now, this H c is incoming total r is reflection coefficient also popularly called albedo. Albedo value will show how much is reflected back to the atmosphere of the total incoming radiation. And then we will have to add some back radiation or rather subtract some. So, we can write this as minus H p this part radiated from the water surface. So, if there is a lake here the amount of heat radiated back will be H b and r represent the reflection back to the atmosphere. So, the net heat coming in or received by the water body can be written as incoming solar radiation which we can obtain 1 minus r. So, this is the amount reflected that means this is the amount which is absorbed H c 1 minus r and out of that H b is again radiated back. So, this net heat inflow H n is obtained as H c 1 minus r minus H b. So, this we can obtain H g is the amount of heat which is transferred to the ground. So, H n is easy to obtain H g is the amount of heat which is transferred to the ground knowing the ground temperature and the water body temperature this is also easy to obtain. H s is the storage within the heat storage within the water body knowing the water body temperature and the change we can obtain this also easily. H i heat advected out of the water body is again knowing the amount of water which is going out of the water body we can estimate this also very easily. So, other terms are easy to obtain except H a. H a is the sensible heat transfer from water to air and it is very difficult to measure it that is why we typically relate it with the evaporation itself and the equation which we use is beta times where this rho l e l is nothing but the heat energy being used for evaporation and beta is known as the bonds ratio. So, in other words you can say that this is the ratio of the sensible heat transfer between water and air and the heat used for evaporation and this has been obtained empirically as difference of the water and air temperature multiplied by atmospheric pressure divided by delta e. So, these units of course, will be centigrade for temperature. So, this is temperature in degree c temperature of water and air e w e a we have already seen these will be in millimeters of mercury and p a also atmospheric pressure millimeter of mercury. So, once we obtain beta we can obtain H a or we can write H a in terms of the heat of evaporation and the bonds ratio. So, using all these values we can finally, get an equation for e l as H n minus H g minus H s and as we have discussed all these 4 quantities are comparatively easier to measure and therefore, obtaining e l from this equation is quite straight forward. So, using water balance or energy balance we can obtain the lake evaporation e l. So, we have seen 3 different methods one measurement using a pan one based on some empirical equations derived for some local conditions, but empirical equations we may be able to derive for our own area of interest also. And then the theoretical equations which are based on water balance or energy balance they will need measurement of certain quantities, but these quantities are not very difficult to measure. So, we can use one of these equations to find out the evaporation. The next term which we want is evapotranspiration. So, evapotranspiration as we have seen is the combination or sum of evaporation and transpiration and therefore, there are some additional complications involved in determination because transpiration depends on the plants growth, what is their water requirement, what is the stage of growth. So, evapotranspiration is comparatively difficult to measure or estimate compared to evaporation. Again there are techniques which are similar to what we have used for evaporation. So, we can have measurement or we can have empirical equations or we can have theoretical equations. So, same as in evaporation, but in evapotranspiration there is a very fine distinction between what we call potential evapotranspiration and the actual evapotranspiration. The potential evapotranspiration is the evapotranspiration which will be occurring if water is available. But sometimes if we look at the ground and the soil below this, in the root zone of the plant there will be some soil moisture. Now, if soil moisture is not available then transpiration will not take place. Below a certain soil moisture the plants will not be transpiring and we have to define. So, in a soil we have looked at the terms field capacity and there is another term related to the type of vegetation which we call permanent wilting point. Permanent wilting point is the amount of soil moisture below which plants will not survive and field capacity as we have seen is the maximum amount of water which the soil can hold under gravity. So, potential evapotranspiration is the one which we can estimate using these methods. Actual evapotranspiration will depend on the field conditions. So, we will look at some of the methods of estimating the PET. The actual evapotranspiration AET when compared with PET will decide on whether plants are able to get enough water or not. So, the evapotranspiration and some measurement of infiltration and equations for infiltration we will look at in the next lecture. So, in today's lecture we have looked at various methods of estimating evaporation. We have looked at some methods which are based on measurement. So, we measure the evaporation from a pan and we correlate the evaporation from a nearby water body with the evaporation in the pan. And there is a pan coefficient which we use for this purpose. We looked at two different pans one used by US weather bureau other in India and we looked at their pan coefficient. So, also which are 0.7 and 0.8. Then we use some empirical equations to obtain evaporation for a particular area relate the evaporation with the wind velocity and the vapor pressure difference. Then we also looked at some theoretical methods which are based on water balance or energy balance. So, next time we will look at similar methods used for evapotranspiration and some methods used for infiltration.