 So, today we will continue to discuss some of the abstractions from the precipitation. As we have seen we can also call them as loss because these are the amounts which are taken out of the precipitation and the rest goes to runoff. So, if you are interested in runoff then these parts as act as losses. We have looked at evaporation and how to measure it how to estimate it using some empirical or theoretical equations. Today, we will look at transpiration, combine it with evaporation and we will look at evapotranspiration and we will also look at the infiltration. So, let us start with the evapotranspiration which is also known as the consumptive use. So, it is the sum of evaporation and transpiration evaporation from the land surface, transpiration from the plants and we can again as we had in evaporation we can have evapotranspiration estimated by measurements or we can use some empirical equations and we may have some theoretical equations. So, in measurements evapotranspiration is typically measured by using water balance measuring other components and then estimating the evapotranspiration. There is an instrument which is known as a lysometer which is nothing but a closed tank in which some plants are also placed and then to maintain a constant moisture we need to supply periodically some water. The amount of water will represent the evapotranspiration in that time period or we can have some field plots in which under very controlled condition we can estimate what is the irrigation, what is the runoff and then using a water balance we can find out what is the evapotranspiration. The empirical equations typically based on the crops and the amount of heat energy available these are the two main factors which are taken into account when we derive an empirical equation which relates the evapotranspiration with the type of crop, the stage of growth of crop, the amount of heat energy available which typically depends on the sunshine hours. So, it is the total amount of number of hours in a day for which sun is shining and therefore, heat energy is available to us. So, some of these terms will be used in empirical equations. In theoretical equations they also depend on the crop type and the heat energy but they have in addition some other parameters which we have to estimate and using a purely theoretical approach we can derive these equations. So, let us start with the measurement of evapotranspiration. The first method which is typically used is known as a lysimeter which is an air tight tank filled with soil and some plants and this will be placed in the at the ground level. So, that the level of soil in the lysimeter and the surrounding area is the same. The plants in the lysimeter should be similar to the plants which are outside the area. So, that the transpiration is almost same. So, the lysimeter of the air tight tank should represent the nearby conditions the soil, the plants and so on. Now, the amount of moisture in this lysimeter is monitored. So, moisture content is monitored and periodically we add water to maintain the soil at a constant moisture and the amount of water which is added represents the evapotranspiration. There are some precautions which we have to take. First thing is of course, it should be accurately represent the surrounding area. So, accurate representation of the surrounding soils is a requirement. The plants should be similar the soil should be similar. Naturally, it is expensive to install and monitor. So, typically it is not used very often, but if we are interested in higher accuracy results and we are not concerned too much about money, we can install lysimeters in the field and measure the amount of evapotranspiration from that. The time consuming of course, because we have to we have to install lysimeter and keep on measuring the evapotranspiration on a daily basis or monthly basis whatever time period we are interested in. The second method which is used is known as the method using field plots in which we have these plots which may be about 4 meter by 2 meter size. So, 4 meter in length, 2 meter in width and then there will be some nozzles which will put water on this field plot. Then there will be some runoff which will be measured. The amount of water which is infiltrated can also be measured. So, the amount of water coming in then there will be some transpiration from these plants some evaporation. So, the field plots are under very controlled conditions and if we measure the other quantities then we can estimate the evapotranspiration E t as p which is the precipitation plus irrigation. So, if we know the amount of rainfall and these nozzles if we are doing it in the lab we can do it like this or if we are in the field we can measure the actual precipitation and the irrigation rate. So, there is some irrigation water applied to this plot. So, the rainfall plus irrigation will be the net inflow into the field plot. Then we will have to measure the runoff and if there is any increase in soil moisture. So, this increase in soil moisture is typically measured below this level. So, the amount of evapotranspiration can be obtained by water balance such that if we know the precipitation which we will typically know by using rain gauges applied irrigation water that we will also know runoff we will have to measure and then increase in soil moisture also we will have to measure and using this water budget we would get the evapotranspiration. There is one more component which is typically used in this equation as I have shown this infiltration or we can say that this is the water loss to ground water or ground water recharge. So, out of this infiltration part of it will be retained in the soil that will increase the soil moisture part of it will go down and recharge the ground water. This part typically is very difficult to estimate and that is why I have not shown it here. Typically what we try to do is maintain the soil below the plot at the field capacity or below the field capacity. So, that ground water recharge is minimized and therefore, typically we will ignore this and use only these these terms precipitation irrigation runoff and soil moisture which can be measured easily and evapotranspiration can be estimated. So, using these two methods the either lysimeter or field plot we can estimate the evapotranspiration by measurement. Then measurement typically are not either very easy or they are time consuming or they are expensive. So, generally people have gone for empirical equations in which they have studied over a certain area the amount of evapotranspiration and try to correlate it with the factors on which it depends for example, the crop type of crop the growth of crop and the sunshine hours. So, we will look at these empirical equations and the two empirical equations which we will look at here although there are various other equations also, but the one which are commonly used are known as the Blenichradial and the Thronthwaite equation. Now, in the Blenichradial equation we have an equation which relates the evapotranspiration. This 2.54 factor comes because the original equation is in FPS units and they are two terms k and f on which these evapotranspiration depends. Now, whenever we talk about evapotranspiration we should keep in mind that this is potential evapotranspiration which is typically denoted by P e t. The actual evapotranspiration will typically be less than this depending on what is the amount of soil moisture available. So, this equation relates e t with 2.54 as I said this is originally it was an inches per day and then it was converted to centimeter. This is either per day or whatever time period. So, I will write per unit time period. Typically a month is taken. So, this time period would be in a month. In the original equation this 2.54 as I said was not there, but e t was k f in inches. Now, k is a factor which is a function of type of crop. For example, for rice k may be around 1.1 and if you have wheat it would be typically about 0.65. For natural vegetation it varies over a wide range 0.8 to 1.3 depending on the density of the vegetation. So, this factor k can be obtained from the type of crop grown in that area or the vegetation which is growing in that area. F is a factor which is known as monthly consumptive use. Consumptive use as we have seen is also another name for evapotranspiration. When we sum the monthly consumptive use factors for each month, then we will get the value of f and the formula for f is given as summation of p h t f bar over 100. This 100 is there because p h is a percent. So, this p h by 100 is a fraction. The definition of these terms is p h is the monthly percent of the annual daylight. Daylight hours or sometimes we call them sunshine hours is the amount of daylight available in let us say a particular day or a particular month or annual means in the total in the whole year. So, for each month we will have values of what is the daylight hours in the month expressed as a percentage of daylight hours in the entire year. This again is a function of latitude. So, as we know as we increase the latitude number of daylight hours will typically decrease and its value is typically. So, let me first say that this p h decreases with increase in latitude. So, typically at 0 degree we will have a higher value and at let us say 40 degree north or 50 degree north we will have a lower value and the range of f is about 6 to 10. So, in a particular month it also depends on the month. So, for example, for January it may be a smaller percentage. For summer months it will be a higher percentage and as you can see typically if you assume uniform over the whole year then the fraction will be 1 by 12 into 100 percent. So, 8.33 percent that would be if the sunshine hours are uniformly distributed throughout the year then each month will have about 8 percent of the annual sunshine hours. But, since sunshine hours vary with month some months will have a smaller value than 8 some will have a larger value than 8. So, typically it will vary from 6 to 10 depending on the latitude and the month summer it will be higher latitude 0 degree latitude this will be higher. So, this fraction p h and then we have this t f bar. So, multiplication of p h and t f bar is the is summed up over the entire month or over all the months then we get f. t f is the mean monthly temperature and it was used in degree for an height in the original equation. So, we will keep that degree for an height. So, using the mean monthly temperatures for each month and the percentage p h we can find out this factor f and then using the Blanik-Schilderl equation we can find out the evapotranspiration. Of course, this k has to be estimated based on the crop type and f we get from the formula. So, this gives us an empirical method for finding out the evapotranspiration. Thront weight equation is a similar equation where we have an equation like this 1.6 l a 10 t bar over i t to the power a. So, this also has similar kind of form with lot of these factors l a is an index for number of daylight hours which as you can see is similar to what we had used earlier daylight hours, but here it is defined little differently again it will be a function of latitude and month. This also has a similar tendency decreases with latitude and the typical variation is 0.8 to 1.3. So, there are tables available for different latitudes and different months, January, February and so on, latitudes 0 degree, 10 degree north and so on. So, we will have these values of l a given in a tabular form and you can look up from here what is the value. So, this is an index which denotes the amount of or the number of daylight hours for a particular month. T bar as we have used before is a mean monthly temperature, but now we use degree Celsius rather than degree foreign height. The other term i t is an heat index and this is defined on the basis of the mean monthly temperature, summation over all the months. T bar again is the mean monthly temperature for the month i. So, i will go from 1 to 12 for the entire year. So, i t is an index which really is called the heat index which tells you how many daylight hours or how much will be the temperature mean temperature for each month summed up for the whole year. There is a factor a which is again an empirical index or we can say an exponent which is a function of i t. It has been found that a can be given as a constant about 0.49 plus a cubic equation a linear term. Then we have a quadratic term and then we have a cubic term. So, knowing the heat index we can compute the value of a from here mean monthly temperatures are known to us. L a can be looked up from the table and this will give us the potential evapotranspiration using the throntwit equation. The empirical equations are good, but they are valid over a particular area and to apply them to some other area we have to be careful. We have to look at these factors and take a different value may be for a different area. So, that is why equations which are based little more on theory are preferred and one of the theoretical equations which is commonly used is known as the Penman's equation. In the Penman's equation the evapotranspiration is written as a factor a times h n plus another factor gamma times e a given and divide by a plus gamma. So, this e t is the potential evapotranspiration and again the units can be taken as millimeter per day. So, the time unit the time unit can be millimeter per day typically every day we can find out what is the potential evapotranspiration. H n is the net radiation which we will see little later. A is the slope of the saturation vapor pressure curve. So, as we have already seen the saturation vapor pressure which is denoted by e w is a function of temperature and typically follows a curve like this. The slope of this curve at any point is the factor a. Now, sometimes there is an equation or relation between e w and t which can be used to obtain this factor a. So, e w can be written as 4.584 exponential of 17.270 over 2. So, this t is the temperature and you can obtain this e w using fitting this curve, but most of the times this curve will be given in a tabular form and the slope a also will be given in tabular form. So, slope of this line a which is d of e w by d t can be found from this equation or using the tables or the graph we can find the slope a. So, I will write it here a is the slope of saturation vapor pressure. The units of course will be typically millimeter of mercury per degree centigrade. The other factor which we use is the gamma which is the psychometric constant and its value typically is taken as about 0.49 millimeter of mercury per degree Celsius. So, these are the these two factors a and gamma e a is a function of wind speed and the vapor pressure deficit as we have seen earlier in evaporation. The evaporation depends on wind speed and the difference in vapor pressure at water temperature, saturation vapor pressure at water temperature and the actual air vapor pressure. So, this can be related or this was given by an equation 0.35 1 plus u 2 by 160 e w minus e a. This as earlier this u 2 represents the speed 2 meter above ground e w and e a we have already discussed. These are the saturation vapor pressure at water temperature actual vapor pressure in the air. So, this is the saturation the vapor pressure deficit. This is wind speed factor which represents the amount or the speed with which we carry the saturation of the saturated air vapor out away from the water body. So, this is the e a is the evaporation which is related with wind speed and the vapor pressure deficit. The important term here in the Penman's equation is h n. h n can be defined in terms of net radiation, but not in terms of heat energy, but in terms of evaporation depth. So, in terms of there will be some millimeter we can use for depth units. So, millimeter of evaporable water per day which means that if this is the net radiation how much depth of water it will be able to evaporate in a day. And it can be related with an equation like this r is the reflectance or the albedo. Then we multiply it with a modified modification a plus b into n by n. Then we have the Stefan Boltzmann constant square root of e a which is the vapor pressure in the air. And then we multiply this by another modifying factor 0.1 plus 0.9 n by n. r as we have seen is the reflectance or the albedo. So, this and the value for r is given for different materials. For example, for water r is typically about 0.05. For land it may vary depending on the land use, but typically about 0.25. And if you have let us say snow it will have a very high reflectance and a value as high as 0.5 can be typically used. This sigma term represents the Stefan Boltzmann constant and its value is given as around 2 times 10 to the power minus 9. So, this sigma value is used in combination with the absolute temperature. And as we know it is T a to the power 4. So, this T a is the mean air temperature in degree Kelvin. As we know the Stefan Boltzmann equation the radiation radiated energy is proportional to the absolute temperature to the power 4. The other terms which are used in the equation one of the most important terms is the incident solar radiation. Because this governs how much energy is available for evaporation at that location. This will also be a function of latitude time of year. And this is also expressed in millimeter per day of evaporable water. So, the amount of heat energy available how much depth of evaporation it will cause in millimeter per day that is H a. Function of latitude and time of year as we have discussed are already this will H a will decrease. H a decreases with increase in latitude. So, at 0 degree it will have a higher value than 10 degree north 20 degree north it will have lower value. Similarly, time of year in summer H a will be higher and winter. So, depending on the time of the year and the latitude we can obtain H a typically it will be given in a tabular form. And similar to what we have seen earlier we have latitude month and we will have H a values given in a table like this. So, we can get the H a value from there. There are some constants used in this equation for example, a b and n capital N. These are some constants which have been defined by Penman's equation. A is a function of latitude and typically given by about 0.29 cosine of phi where phi is the latitude. B is generally taken as a constant and around 0.5 or 5 2 is the value n is the actual sunshine hours. So, number of actual sunshine hours and capital N is the maximum possible sunshine hours. So, n is number of sunshine hours actually occurring at that time and n is maximum possible for that period number of sunshine hours. N of course, maximum possible sunshine hours is again a function of latitude and the time latitude and month and typically varies from 8 to 16. For example, if you have winter months at high latitudes number of daylight hours may be as low as 8. If you have summer months near the equators number of daylight hours may be as high as 16. So, knowing all these values we can estimate the evapotranspiration using the Penman's equation sorry H N and then E t using the Penman's equation. So, these are Penman's equation is little more theoretical and from place to place you can estimate different parameters and obtain the evapotranspiration. So, evaporation and evapotranspiration can be combined evaporation as evapotranspiration or consumptive use. We have looked at different methods may be measurement empirical equations or theoretical equations to estimate this. The next component of abstraction will be which we will take will be the infiltration which is the component which is going below the surface of the earth and the amount of infiltration which goes or which infiltrates into the soil will be taken out of the precipitation evapotranspiration will be taken out of the precipitation and the rest we can say will go as runoff, but after satisfying some initial abstraction which is depression storage and some interception. So, infiltration measurement and its estimation using some empirical or semi theoretical equations will be our next topic. So, in infiltration as we have seen when precipitation occurs part of it will runoff part of it will infiltrate. So, this infiltrated water will either stay in the top soil layer here or it will go deeper and recharge the ground water as deep percolation. So, when infiltration occurs if you look at the soil moisture suppose there is some initial moisture content in the soil theta i. So, what we are plotting is theta axis and depth below the ground level. So, initially let us say we have a constant value of the moisture content theta i as water falls on this surface. It would increase the moisture level near the surface. So, we will have a zone which we can call saturation zone in which the soil will be more or less saturated. We can say that the entire porosity may be filled with water. So, if porosity is plotted here then the entire soil here is more or less saturated with water. Then there will be some unsaturated zone here and there will be a sudden drop. So, the second zone will be unsaturated it will have partial air saturation partial water. So, this will can call the transmission zone. So, water is being transmitted or infiltrated and partial filled with air the voids are partially filled with air and partially with water. Then we have a third zone here which we can call the wetting zone and there will be a sharp front here a wetting front. So, below this level the soil will be existing at its previous or original moisture content. So, there is really no effect of the precipitation felt beyond the wetting zone or this wetting front. Wetting front is a very sharp change in the moisture content and beyond that the effect of precipitation is not filled. So, this is the mechanism of infiltration or this is the variation of the soil moisture below the ground surface. Now, once we want to estimate the infiltration we should be able to solve this equation which governs the flow in this area, but this is a very complicated equation because water is not filled or the all the voids are not filled with water there is some air also. So, the conductivity of this material depends on what is the saturation. So, we call it unsaturated flow where the conductivity is a function of the moisture content and the equations are highly non-linear and therefore, difficult to solve. So, we can use some measurements or we can use some semi theoretical equations to estimate the infiltration. Filtration of infiltration is typically done by instruments which are known as infiltrometers. For example, we can have the ground surface and we can put a ring in the ground. We can fill it with water and then we note down how fast the water level is going down in the ring. We fill it or we keep on filling it adding more water to maintain the water level and the amount of water which is added to maintain the continuous constant level would be giving us the rate of infiltration. Typically, a simple infiltrometer so this we will call it simple infiltrometer. The typically dimensions of the rings are given for example, a general generally used ring may be of 30 centimeter diameter, 60 centimeter high or long and 50 centimeter deep. So, total may be 60 centimeters it may be driven 50 centimeter below the ground surface and the water level is generally around 5 centimeters. So, water depth 5 centimeters. So, using these standard sizes we can fill it with water and note down how much water is to be added to maintain this water level. The problem with this ring is that near the edges the flow is not vertical. So, the area of the ring will not represent the area of the flow typically because of this behavior. So, there is a modification in the simple infiltrometer and sometimes we use what is known as double ring infiltrometers. In double ring we have an inner ring and an outer ring. So, this is the ground level we have an outer ring and then we have an inner ring in which we will maintain a level we will add more water to maintain a continuous constant water level here and the amount of water added will denote the infiltration. But here because of the presence of the outer ring the flow will be nearly one directional or one dimensional in the entire area and therefore, this will give us a better measure of the amount of infiltration which is taking place. So, these infiltrometers either simple or double ring can be used to estimate the infiltration the one major objection with these infiltrometers is that they do not simulate the impact of rain. So, in field if you have let us say this ground level there are rain drops falling on the ground surface and because of the impact of these rain drops the soil gets disturbed the some of the fine particles they may get washed away and get deposited into the pores a bigger pores and that affects the infiltration. The other objection with the infiltrometer is that when we are driving them in the ground it will disturb the nearby soil and therefore, the amount of infiltration which we get may not represent actual infiltration. So, these two objections one is the impact of rain drop is not simulated the other is that when we are driving these inside the ground the soil nearby area gets affected and therefore, it does not represent undisturbed conditions. Therefore, there is another method which is commonly used although little more expensive is known as the rainfall simulator. Similar to the field plot which we discussed for evapotranspiration rainfall simulator is also carried out under controlled conditions a plot again size generally would be about 4 meter by 2 meter the rainfall will be simulated by putting some nozzles above this area. So, as we saw in evaporation experiment also we can do similar setup with put some plants here and measure the evapotranspiration but here our interest is measuring the runoff. So, from this plot there will be some runoff and there will be some precipitation which of course, is known to us the height of the nozzles from the plot is generally kept as 2 meter and this will also simulate some impact of the rain drops. So, when rain drops fall on this plot they will have impact here and the other advantage is that since we are not driving anything into the ground the soil is undisturbed. So, by measuring the precipitation and the runoff we can know what is the infiltration so this rainfall simulator takes care of the objections of the simple or double ring infiltrometer that the raindrop impact is not simulated in the first case and the soil was disturbed. So, both those are avoided in the rainfall simulator. So, this is preferred over the infiltrometer but of course, this is more expensive. So, depending on what is our aim we can go for either this or we can go for double ring typically double ring is preferred over single or simple ring. Now, the rate of infiltration is not constant with time the rate of infiltration typically decreases with time and there are various reasons for this for example, because of raindrop impact the soil may get compacted the pores may get filled with fine material therefore, rainfall the infiltration rate will decrease. The other thing may be that as the soil gets more and more moisture its capacity to infiltrate will also be reducing. So, we should be able to predict this infiltration rate variation with time that is the this curve. So, as to know how much water will be lost in infiltration there are various methods which can give us this curve all are typically based on if you look at the theory. Theory says that the amount of water basically it is the Darcy's law and if we write it for a soil we know that here we have ground level here we have the ground water table. So, the soil in this area is unsaturated. Now, during infiltration we have seen that part of the soil gets saturated, but most of it remains unsaturated. So, the Darcy's law can still be used where psi is the pressure head and z is the elevation, but the only problem is now that is k instead of being a constant the conductivity was constant when the soil was saturated is now a function of the pressure. Typically, in unsaturated conditions psi will have a negative value we call it the suction. So, negative pressure is called suction. So, this equation as we have discussed earlier is non-linear because k depends on psi and then we have partial of psi here with respect to z. This is assuming a one dimensional vertical direction infiltration which will be generally the case. So, theoretically solving this equation is not very easy and therefore, lots of semi theoretical equations have been proposed by assuming something and then solving this equation. So, some of these equations can be written like this Horton's equation. Horton's equation says that the decrease in the infiltration rate or the capacity. So, let us first define this term infiltration capacity we will call it F c. So, the capacity is the amount which can be actually infiltrated the actual infiltration rate will depend on what is the amount of water available. So, if the precipitation is more than infiltration capacity then infiltration will be equal to rate of infiltration will be equal to infiltration capacity, but if precipitation is less than the capacity then actual infiltration will be equal to whatever is the precipitation. So, whatever equations are derived they are derived for infiltration capacity F c versus time and as we have seen it decreases with time and in the Horton's equation we write F c at any time t we relate it with its final value. A steady state value which we can call F c infinity and an initial value F c 0. So, F c 0 is at beginning and F c infinity will be after a very long time. So, this equation given by Horton is an exponential equation where steady state value is this initial value is this k f is a constant for this infiltration which will decide how fast F c is decreasing. So, if large k f then F c is decreasing very fast if it is small then it is decreasing slowly. So, that will be a function of the soil type. There could be other equations for example, there is an equation which is known as Philips equation which also relates the variation of F with time and is given as F c equal to F c infinity S is another soil property which is known as sorptivity. F c infinity is generally taken as equal to k which is the saturated hydraulic conductivity. So, F c can be given as k plus S by 2 t minus half. There could be lot of other equations for example, there is one model which is known as green amped model which assumes a plug flow. So, the moisture profile below the ground instead of being like this is typically assumed to be in the form of a plug flow or a sharp interface like this. So, this will be the wetting front idealized wetting front because we are approximating the actual moisture profile by a sharp front and the length of the profile or the depth to which the soil is saturated will depend on what is the initial moisture theta i what is the saturated moisture let us call it theta s. So, difference of theta s and theta i the delta theta into L. So, L delta theta should be equal to whatever is the infiltration rate let us call it F delta t. So, this will give us the depth of penetration of the moisture front, but we will not discuss these models here Hortons or Philips model typically will be sufficient for our purpose. The only problem is that the parameters are difficult to estimate for example, in Hortons we need to estimate 1, 2 and 3. So, these three parameters need to be estimated similarly, in Philips also soft activity hydraulic conductivity have to be estimated and estimation of these may not be very easy. So, a number of times some simplifying assumptions have been made one of the assumptions uses infiltration indices and the two common indices which are used are known as the phi index and the W index. Now, these represent the average infiltration rate for example, the phi index if you have a rainfall hyatograph like this time versus intensity and we know the losses then we draw a line here in such a way that this volume is equal to the losses. Then this line is will be known as the phi index the value will be known as the phi index and the effective rain this will be the effective rain. So, knowing the losses and knowing the hyatograph we can find out the phi index by making this area equal to the losses and then the remaining portion will be the effective rain. And similarly, we define a W index which is also based on the precipitation runoff and the initial abstraction and we divide it by an effective period which is rainfall excess. So, this we can call effective rain or we can also sometimes call it rainfall excess which represents the amount of rainfall which causes runoff in this case. So, these two indices phi and W indices have been commonly used to represent the infiltration. So, in today's lecture we have looked at evapotranspiration and infiltration various techniques for measuring them some empirical theoretical or semi-theoretical equations to estimate them. So, this finishes the abstraction part. So, we have looked at all the three or other initial losses also. So, we have looked at initial losses which consist of the depression storage and the interception loss. Then we have looked at evaporation evapotranspiration and infiltration various methods of estimating or measuring them.