 various methods for computing reference crop flow of transportation and we had decided that we will look at all the methods which are proposed by the FAO. We had seen the Blanic Ritual method, we had gone into the various aspects of Blanic Ritual method which are proposed by the FAO. Before we go to the next method which is the radiation method I would like to give you the various nomenclature which the FAO has used in all these methods they have used this climatological nomenclature which helps in putting these climate variables into different categories as wherever the data is not available it was felt that it is better to take a range and a nomenclature is used to express these ranges and that I thought would be better if we at least look at how they have been differentiated, how they have been put in these ranges. The various major climatological factors temperature, mean temperature is used, the mean temperature is the average of maximum and minimum temperatures and most of the places you will find that normally the two temperature readings are taken, temperatures recorded continuously but out of those values which are recorded two values are picked up one which is the maximum observed value and the other which is the minimum observed value. The mean temperature is, mean temperature is nothing but if you have maximum temperature and you have minimum temperature if you take the average of those two values that is what is the mean temperature. When the mean temperature is more than 30 degree centigrade then the the conditions are known to be hot when the mean temperature is less than 15 degree centigrade is called cool conditions. Similarly humidity, in the case of humidity you will find some methods, they require the relative humidity, minimum relative humidity to be used and some other methods require the mean relative humidity to be used. So while using the relative humidity, minimum relative humidity these are the various climatical levels which have been used low, medium, high and these are the various ranges of the levels which are associated levels for the minimum relative humidity. Now the mean relative humidity these four levels have been defined low, medium low, medium high and high and these are the associated ranges less than 40 percent, 42, 55 percent, 55 percent to 70 and greater than 70. Similarly the wind again they are two different units which are used to express the wind conditions one is in meters per second and the other is when you are using the the wind run for the whole day that situation is expressed in terms of kilometers per day. So there is only a conversion factor which is differing the two. In one case again the other average the wind speed can be instantaneous because when you are observing you are observing the instantaneous values but then if you average them out over the whole day then you can express them either in the form of meters per second or in terms of the average wind run for the whole day what is the wind run in terms of kilometers per day, okay. So these wind conditions are expressed in terms of light, moderate, strong, very strong. Most of the time you will find that these conditions are picked up from the weather reviews, every area has the published records because these conditions are used only in those situations where you do not have the actual observed data available and you are you are using the average conditions which are influencing the vapor transpiration activity to a great extent. So in the absence of those actual values you are using the average values and since these average values are either average overtime or their values which are representative values for that area is when you look at the weather records, the weather reviews which are normally published by the local meteorological office you will find that they are available on the monthly levels or those records are not in the form of actual data, the instantaneous data they are in the form of average values. So these are the average conditions, there is a reason that these average conditions are defined so that you can make use of these average conditions and you can incorporate them while computing the vapor transpiration values or for the time being we are discussing only 80 knot which is the reference crop vapor transpiration value. So these are in the case of wind, sometimes you might be getting wind in relative terms that you are having the wind conditions which are light and there might be a corresponding explanation that if it is what are the light conditions, light conditions are when you can experience the wind on your face. Moderate conditions there will be conditions when a paper can blow. So you might be having some thumb rules to decipher these conditions or there might be some conditions which you can express in terms of the actual happenings and you can designate these conditions, general conditions with respect to those occurrences. If you do not have the the records available in terms of the actual values or the average values so even that is possible. Similarly the other parameters radiation, the radiation can be expressed in different forms it can be either in the form of sunshine hours and if it is in the form of sunshine hours it will be the end by end ratio we will come to these terms later after a while. These three conditions are expressed low, medium and high and these are the ranges then cloudiness and if it is if the radiation is expressed in the form of cloudiness then there are two ways by which the cloudiness can be expressed, there is one system which is known as tenth system and there is another system which is known as octa system. So these two ranges are given and these are the nomenclatures low, medium and high and these are the corresponding levels. Now let us come to the next method of calculation of ET0 which we had seen that in this method you have the observed data on temperature and sunshine and the radiation data can be used if it is available, if it is not available you can use some relationships for this particular data. In this method this is the expression which is used to represent the radiation method and this ET0 which is the reference crop of upper transpiration for a period under consideration expressed in millimetres per day is a function of R s which is the solar radiation in equivalent evaporation, solar radiation can be expressed in many forms but in this particular expression the solar radiation is converted into equivalent evaporation expressed in millimetres per day and W is the weighting factor which depends on temperature and altitude and C is the adjustment factor which is dependent on the mean humidity and daytime wind conditions. So again you will find that if we compare this with the expression used for the Blaney Cradle it looks a similar expression. In all these methods you will find that a factor has been used which is basically the improvement which has been done on the method. This factor because there are in all these methods it has been found that there are some of the factors which are very active and they are making lot of difference. They might not be making difference in terms of the the computation of ET0 when the conditions are within the condition within the range for which the method has been used or for which the method has been formulated but when you go beyond those ranges then the method was not performing very well. So there are few experts or a team which was interested with this particular job they have tried to look at all these methods and go beyond their recommended ranges and see how they perform in those ranges in those areas in which they were not developed or which were different from where they were developed and that is how they have come out with some recommended additional constraints or additional additional factors which can be incorporated and some corrections can be made. Let us go into the various elements that how do we find out the various elements of this equation? First of all the solar radiation R s when we want to know R s, R s is basically let me use this if we this is the sun, now from the sun this is what is the cause of the solar radiation the rays which are coming and travelling towards the the earth, if this is the earth the radiation which is coming up to the atmosphere if this is the level beyond which the atmosphere makes lot of impact then this component is sorry this is this component is R a the solar radiation which is approaching the atmosphere which is reaching the atmosphere and this solar radiation R a is basically a function of only two things, one latitude what is the latitude of the place which you are interested in which you are considering to find out how much is the solar radiation which is which is coming to that location and the second is which is which is the period in question, so the location is defined with respect to the latitude and the atmosphere which hemisphere you are in the latitude with respect to the atmosphere will pinpoint which is the which is the location in question then the variation with respect to the the period, so there is a a table which is a unique table which is a fixed table which gives the extra terrestrial radiation R a for different locations on the earth and that is the table which is with respect to latitude and the the southern hemisphere northern hemisphere and for different months these are the some of the values which are picked up just to to show you because the table in the full form this is the table which gives the R a value for this is the latitude the southern hemisphere northern hemisphere January to December January to December and these are the different values, so once you know the latitude you know in which hemisphere it is you can use this table to find out how much is the solar radiation approaching the atmosphere, so once R a is known this is the this is the maximum radiation which can come which can reach the earth at a particular time for that specific location, this remains fixed but what happens some part of this radiation is absorbed by the atmosphere, so it depends on the conditions of the atmosphere, it it is a function of atmospheric conditions how much of this radiation will get absorbed and how much will be scattered, so there is a there is a part which is which is reaching the earth surface that is known as the r s that part is known as the solar radiation, this can if it is if it is it can be direct directly made it is fine otherwise it can be obtained from this expression where you are using the the sunshine ratio, this N by N is the sunshine ratio which is expressed as the ratio between actual married bright sunshine hours and maximum possible sunshine hours, now this maximum possible sunshine hours again as we have seen in the previous lecture that this is something which is fixed, the maximum sunshine hours again is a function of which location, what time of the year, so there is a table which gives the maximum the mean daily duration of maximum possible sunshine hours at different latitudes and for different months and this table give you a value which is N value which is the maximum sunshine hours possible sunshine hours which is the difference between the the sunrise and the sunset which remains fixed, so it is independent of whether it was cloudy or it was not cloudy, you are looking at what are the possible if there is no if there is no cloud then what is the possible number of sunshine hours that is what is given by this table and the small N which is used here the small N which is used here is the actual married bright sunshine hours that is basically there is a possibility that if the the sunshine is is not of the solar radiation is not reaching the earth surface is because of the fact that there is some cloud prevalent at the particular location, so the activity of the upper transpiration will be totally influenced by the number of sunshine hours which were prevalent at that particular time or during that duration if you are taking a particular month in that month how many sunshine hours were there and how many sunshine hours were possible that ratio is used to find out what is the solar radiation which is reaching the earth surface, so once you know what is the Rs in which you have taken the taken into account the effect of the clouds how many for how long the clouds were there to find out the small N value there are various ways by which you can know what is the N value, there is a equipment which is quite often used which is known as in general the sunshine recorder the campbell stroke sunshine recorder is equipment which is quite often used to find out how much is the the number of hours which were actually sunshine hours in a particular day and the the way it is done is that you use a strip of paper and you have a globe a ball through which you let the rays of the sun pass the paper is attached behind this ball so it has the same effect as when you take a lens and burn the paper it has a similar effect so it will depending on for how long the sunshine was available it will have the paper burned for that duration it can be calibrated and you can at the end of the day you can find out what is the length of the paper which is charged and accordingly you can find out what is the N value, so the actual sunshine hours you can you can make environment on those sunshine hours using the cloudiness can be can be expressed in the form of octas or 10s so this is the relationship between N by N ratio and cloudiness if you have the cloudiness available instead of N by N ratio or the sunshine ratio then you can convert that cloudiness into the equivalent sunshine ratio so that you can use it in the equation to find out the ET naught and this this relationship or this conversion again is available in FU 24 publication on crop water requirement all this material which I am using you can refer to crop water requirement publication or the research paper on irrigation and drainage division by FU they are given all these these relationships and all these details in a very elaborate manner. Now next let us have a look at the weighting factors W which we have because the equation in the equation ET naught is equal to R s into W into C that is what we have the relationship so we have looked at R s the solar radiation, W is the weighting factor which is used to differentiate the impact of temperature and altitude on ET naught. So this table you have the temperature this is the temperature given on this side from 2 degree centigrade to 40 degree centigrade and for different altitudes the altitude varies from 0 to 4000. The values of W are given here you can see here that as we go closer to higher temperatures the factor is nearing approaching 1 that means the conditions under which the the equation the radiation equation has been used or has been uhh has been formulated as such it was more near such conditions this this area where it was closer to 1 where the temperatures are slightly higher on the higher side and even the altitudes are also uhh somewhere in this range from 500 meters to around uhh 2000 or 3000 meters. In this zone where the values can even go to 0.43 when the temperatures are 2 degree centigrade that means the lower the temperature it was felt that it was giving very high results it was over-simulating the values which you were getting they were much more than the actual values that is why awaiting factor of almost uhh half or less than even 0.5 has been recommended. Now coming to the last factor which is the correction factor small c again a table has been recommended a graphical uhh these uhh 4 different figures have been recommended where only 2 parameters are now used one is the relative humidity the mean relative humidity this is r h mean is it visible or I will write here. This particular humidity mean relative humidity is medium to high 55 percent to 70 percent in this uhh figure and when the r h mean is high this is greater than 70 percent then this figure is recommended. Again in constructing all these figures again the regression analysis the stepwise regression analysis has been done and that is how these figures have been obtained by taking each individual parameter into consideration and looking at its impact. The others parameters which are used are the ray time wind conditions the ray time wind speed and there are 4 different wind speeds which have been taken 0 to 2 meters per second 2 to 5 5 to 8 and greater than 8 meters per second. So these 4 are represented by number 1 this is number 1, number 2, number 3 and number 4 uhh these uhh curves depending on these 2 parameters the relative humidity this is the mean relative humidity and the wind conditions the value of c has been recommended. So on this side you have this is basically W into r s but W into r s once you find W into r s after finding out the each individual item you can look at what is the relative humidity mean mean value of relative humidity that can be uhh found out and then you can find out which is the relevant figure the relative mean humidity is high use this if it is medium high use this what is low then this figure is valid if it is low medium this figure is valid then you can find out what is the due U day time wind condition the U day time wind which particular condition is valid accordingly choose the appropriate line and then you can find out what is the value of 80 knot. So having W into r s value available and after knowing which is the corresponding r h mean which has to be used along with the wind conditions you can directly use this go up in this direction if 2 is the the U uhh U day condition then move horizontally and this value the value can be read this value is 80 knot in millimetres per day if you do not want to use the graphical presentation then this can be converted into some tables which can be used in a computer system you can only thing is that you will have to interpolate between the 2 values so the linear interpolation can be done if you get a value uhh which is in between the 2 values because then you will have to give all these points in the form of either equation or in terms of the actual values for different levels. So if you give in terms of the actual values in the form of a table then you will have to have incorporate a interpolation procedure and that can also be done it is not difficult the packages are available where the interpolation is resorted to you do not have to actually use these uhh figures these figure figures can be converted into equivalent tables or in the form of some equations which can be directly used but if you are doing it manually then it is much easier to use these these graphical uhh figures. Now with this uhh the method on radiation is taken care of and this method again is quite it gives reasonably good results and it depends on whether you have the data available which is the required data. Now coming to the next method which is the Penman method this method is the most efficient and most accurate method but at the same time it requires a very very large amount of data. If we again go back to the same figure what is the data which is required for the Penman method you will see that it requires the data on temperature, humidity, wind conditions, uhh sunshine data and as well as the radiation data. This method was put forward by Penman in 1948 and at that time the method was basically it was introduced to find out what is the open surface evaporation later on it was said that the same method can also be used for evapotranspiration because basically the factors which affect evaporation is the same factors which affect the evapotranspiration also. So when you talk of evaporation from water bodies that is something which is the potential evaporation from the water bodies is when you say potential evaporation what we are saying indirectly is that there is no there is no dirt of availability of moisture or we are saying that there is no constraint on the availability of moisture that is why from water bodies whenever you say evaporation is always at the potential rate whereas the other thing is not true if we are talking in terms of the evapotranspiration from the soil surface or from the land is not always at the potential rate because it is dependent on what is the availability of moisture in the roots on top. So when you say evapotranspiration though in all these equations which we have seen so far in all these methods which we have treated so far we are making an inherent assumption that there is no dirt of moisture availability there is no constraint on the moisture availability that is why the ET0 which we are trying to find out the reference clock evapotranspiration it is the potential value it is the maximum value which can take place in those circumstances or in those conditions. So to find out the grass evapotranspiration and that is where I think I am not sure but I think maybe that is the situation in which the grass was thought of to be used as reference evapotranspiration medium where this was done in England and the pen evaporation the penman equation was used to find out what is the evapotranspiration from grass. It was found that by just multiplying the E0 which is the open surface evaporation given by penman if you multiply that by a crop coefficient ranging between 0.6 to 0.8 you can you can get the evapotranspiration for the grass but at the time of this intercomparison or the F14 when they looked at the penman method again they found that is is really very difficult to find out which crop coefficient should be used. In some situations 0.8 was quite uhh quite a satisfactory value but in some situations 0.8 was not it was giving quite high estimates so they have uhh they have used all this information in giving a revised form of penman method the method remains same only they have introduced a revised wind function which we will just discuss. Let us first have a look at basically what is the difference between the penman method in comparison to the other methods. In the penman method two terms have been used in the penman equation one is the energy term and the other is aerodynamic term because it has been seen that whenever you you are trying to estimate the evapotranspiration activity at a particular location in some situations is the the radiation term or is the radiation which is more prevalent for example if the conditions are very calm the weather is very calm you will find that the the energy term will become very important because the the the activity of evapotranspiration will be dominated by the radiation which is prevalent at that particular location. On the contrary there are some situations where you will find that if the conditions are very windy to the conditions are such that the wind and humidity they are influencing the the evapotranspiration activity then the aerodynamic term will be more predominant. So that is the combination of these two terms which will be in a position to approximate or simulate the conditions in a better manner. The level of the or the extent of their involvement is a function of the actual conditions. So if you have a equation which can take into account both these factors then that that that equation will be more uhh useful it will be more accurate and that is the reason that the Penman equation has a better uhh uhh chance of performance or it is its results are much better in comparison to the other equations. Let us try to look at the equation as recommended by Afio which is uhh only a slight modification only in the in the form of this wind function and the C factor has been introduced. This is the equation in which this W into Rn this component is the radiation term, this part this part is the aerodynamic term whereas this part is the radiation term. Looking at the various elements of this equation W is the temperature related mating factor, Rn is the net radiation in equivalent evaporation expressed in millimetres per day. Afio is the wind related function, A A minus E D this term is the difference between the saturated vapour pressure at mean air temperature that is A, A is the saturation vapour pressure at mean air temperature and the mean actual vapour pressure of the air which is E D both expressed in millibars and C is the adjustment factor as we had mentioned earlier also. This adjustment factor compensates for the effect of day and night weather conditions. Now each of these terms how we can compute each of these terms that is what is our next question and that is where you will find that you have if you will ultimately look at this whole procedure you will find that this is quite a laborious uhh thing the terms the number of terms which are involved and these also in turn involve many other terms which have to be looked at but at the same time method has been made quite simple by providing the various uhh uhh relationships in the form of either the graphical representations or in the form of tables and we will have a look at all those uhh things in detail. So we will try to take each of these elements one by one and try to look at what is involved in computing those individual elements and which are the which are the various tables which are available. I think we should leave that to the next class because if we will start that we will not be in a position to finish.