 various components of this equation and we had looked at the pressure deficit was the weighted factors as a wind function and only thing which is left is the net radiation. So to start today with the net radiation, to start with let us see what do we mean by the net radiation. The net radiation is the difference between all the incoming and outgoing radiation with respect to the earth because this is the source, this is the source of the energy which is responsible for the evapotranspiration activity. If you look at this figure, this gives the various components of, so the source is the sun here which is the say source of radiation and we have already seen that some part of this radiation reaches the ground surface but before the atmosphere, a part which is reaching the atmosphere which is known as the extraterrestrial radiation which we had expressed by r a, there is something which is fixed which is which remains same as long as we are looking at the same period in the year and we are concerned with the same coordinates on the earth. So when we are looking from a particular point on the earth and for a particular location in other words and also for a particular duration of the year, the amount of r a, the extraterrestrial radiation will remain same, there is a unique quantity but what happens when this r a, it approaches towards the part of this r a, some part of this radiation gets absorbed in the atmosphere, it gets, some part of that gets scattered, so the part which gets scattered is accounted for in terms of the r s, r s was the radiation reaching the surface, now this r s is the shortwave radiation which is reaching the earth surface, a part of this r s, a part of this shortwave radiation is reflected back into the atmosphere, this reflection, how much it will be reflected back into the atmosphere is a function of this quantity alpha, this alpha here which we have mentioned, the alpha part of r s goes back into the atmosphere or gets reflected into the atmosphere from the surfaces on which the r s impinges. So it depends on what is the surface which is encountered on the earth, was it a water body or was it a cropped area on which the radiation r s impinged upon, depending on that properties of that surface, this alpha will be dependent and this alpha is known as albedo, you must have heard this term in some course earlier in your undergraduate curriculum, this albedo is the alpha which decides, it depends on the reflecting properties of the surface on which this r s impinges. For example if we compare the alpha value, the reflection coefficient will be something to the tune of around 8 or so far water bodies whereas it is up to around 25 for the cropped areas whereas there is lower difference, that means if you are having a cropped area it will be able to absorb, it will be able to absorb less radiation in the soil, more of this will be getting scattered or getting reflected into the atmosphere, that is how you can get the net shortwave radiation. So what is net shortwave radiation? If we, the net shortwave radiation as we are designating it as is r s 1 minus alpha is what is retained. Similarly the other component which is the longwave radiation, this longwave radiation is a function of what is the, what is the status of the atmosphere and what is the status of the earth surface. There is some longwave radiation which is coming from the atmosphere into the soil and there is some component which goes from the soil into the atmosphere and that will depend on the gradient, it will depend on the flux, what is the flux, what are the conditions of the earth with respect to the atmosphere and that is what is accounted for here in the form of this net longwave radiation. This is incoming from the atmosphere into the earth surface whereas there is some part which is going out. Now the net effect if it is, if it is negative in other words if the outgoing is more than the incoming and in general you will find that the outgoing longwave radiation is much higher than the incoming longwave radiation. There is a reason that in the end analysis if we look at the nut radiation, the nut radiation that is the difference between longwave and the nut shortwave. Since nut longwave is the one which is being lost from the earth that is why we have given a negative symbol to this or the sign a lot it is, the sign here is the minus sign. So the nut, nut radiation is the difference between the nut shortwave radiation and the nut longwave radiation. This data which will be involved when you like to compute what is the nut radiation which is available at a particular location. We have already seen this, this specific relationship where you are relating the solar radiation which is reaching the earth surface in terms of the extraterrestrial radiation as a function of the N by N ratio. Since N by N is the major factor which is influencing how much radiation will be absorbed in the atmosphere, r s is a function of these two major parameters. Suppose you have the r s available then the next step is to obtain the shortwave, the nut shortwave radiation which we have said that is dependent on the albedo, is dependent on the reflective properties of the surface on which the solar radiation is oncoming and there is, there is a table available which you can look at shortwave radiation. You can use this table in which you are assuming that this alpha is having a value of 0.25. So there is an assumption and in general this alpha for most of the cropped areas is 0.25, is 25 percent what was what I was mentioning and since we are when we are computing the evapotranspiration from the cropped areas we can ensure that most of the time we are interested in those surfaces where the cropped areas are there, otherwise if we are reusing this equation for some other areas which are either populated areas or urban areas or water bodies then you can choose appropriate alpha value. So this table with that assumption that alpha is 0.25 this is the relationship which is available and you can find out what is the conversion factor which has to be used and knowing the RA you can directly find out what is the value of RNS which is which is equal to 1 minus alpha into RS. So that table can directly give you the conversion factor which has to be used for alpha is equal to 0.25. Then the next is once you have the RNS the only other element is RNL to find out the net radiation and RNL is the long wave radiation which is dependent on many other climatic factors and it has been found that these 3 elements the temperature, the vapour pressure and the n by n ratio these are the 3 elements which influence RNL the maximum. So RNL is found out in terms of these 3 elements or these 3 factors have been obtained and PFEO the way they have suggested this modified Penman equation they have converted they have converted all those different influencing factors in terms of tables you can read directly what is the value of Ft what is the value of the ed and n by n and once you have those values you can directly obtain the RNN value. Let me show there is the other method also which you can use if you do not have these tables available but let us first have a look because these tables are giving a procedure which is much simplified on this particular case this is our table which is giving the effect of temperature on the long wave radiation because how much goes back into the atmosphere is a function of temperature that is the first factor and in this table once you know the temperature you have been given a function which is dependent on T and that value is available here for different temperatures ranging from 0 to 36 you can read the corresponding value of the Ft which in turn is dependent on the temperature which is in Kelvin and a constant sigma which is available. Similarly the other functions are also available the function which is given the variation of Fed which is dependent on the vapor pressure the prevailing vapor pressure is given in this particular table where you have the vapor pressure in millibars and this function is this is the expression used for this particular function 0.34 minus 0.044 under the root Ed and for these values of vapor pressure you can read the corresponding value of Fed and in the same manner the other quantity N by N ratio also there is a relationship which has been made available. So once you have the N by N ratio and we know that N is something which is constant for that location and that part for that particular duration N is something which can be observed that we have already looked into in the last lecture and once you know the N by N ratio then the value can be read so having obtained all these values the factors which are deciding factors for the R and L you can obtain the R and N value and then subsequently you can find out what is the total net radiation. So R and L is the factor dependent on temperature the factor dependent on Ed the factor dependent on N by N ratio and the total net radiation can be now obtained by knowing these two quantities. I just mentioned that there can be a situation where you do not have these tables available or you want to directly go in for equations which if you are not doing this manually you might like to have that in the equation form. This is an alternative equation which can give you the value of net long wave radiation and this is in terms of the net outgoing clear sky long wave radiation which is R and L 0, RS 0 is the daily clear sky solar radiation at surface of earth. Now these are the two quantities which are knowing the assumption that the sky is clear that means there is no effect of the clouds. Knowing these two RS is the solar radiation the actual solar radiation which we are getting so knowing these two quantities you can find out probably we have the empirical constants A and B and these constants are available. We will come to that first let us look at that R and L 0 which is the clear sky net outgoing long wave radiation this is expressed in terms of the eta, sigma, T maximum and T minimum whereas eta is the emissivity of the surface which again you have which is it is dependent on some further more parameters we will come to that. Sigma is the same sigma which we have seen earlier in one of the tables is the constant is known as Stefan Boltzmann constant and its value is 4.8895 into tan star minus 3 joules per square meter by Kelvin to the power 4 and Kelvin as you know is degree centigrade plus 273. Now this emissivity in turn is dependent on the ESDP which is the saturation we have to pressure at dew point. ESDP we were discussing that in the last lecture the dew point is a point on the cyclometric curve and the corresponding vapor pressure will be the dew point vapor pressure the saturation will be pressure at the dew point so that is deciding what is the emissivity. Now in many situations if you do not have the dew point you can and the relative humidity is quite high then you can take the minimum temperatures to be equaling to the dew point temperature. If you do not have that situation where the relative humidity is very high relative humidity is not very high then this would not be possible so in that situation you can use another alternate relationship which uses the mean temperature instead to give you the value of emissivity okay. That means that have now all the relationships which are needed to the only thing is that the some of the constants which we have seen in these equations they are not available the coefficients A, B, A1 and B1 these coefficients are available in some of the areas for USA these are the coefficients which are available for England A and B is not available but A1 and B1 are available and in general it has been seen that the approximate values they can be approximated to these values for most of the other places although there will be some difference and some more work is needed by the scientists to obtain these values if these relationships are to be used because the present relationships which I have given you they are obtained for some specific areas and these values are they are the values which have been published and they are available maybe after some time some more time the other values will also become available. Now okay this is a relationship which so as far as the net tradition is concerned we have seen both the procedures we have seen how we can use the FU recommended procedure and the tables which have been made available and we can use those tables to find out how much is the net tradition value. So having used the having found out the net tradition all the terms of the Penman equation are now known except except this C value which is the conversion factor or the adjustment factor as we know it. This is the only value which is which we have not discussed so far but before we discuss that there is another relationship here which I wanted to bring into your notice. Now there is a relationship between the relative humidity, the air temperature and the dew point temperature which can be used in some situations where you want to get one quantity or the other having known the some of the these quantities. In this the T air is the dry bulk temperature, the T dew point is a dew point temperature and R h is the relative humidity. Now in this expression if you want to get the maximum relative humidity then you can replace the T air the dry bulk temperature with the minimum temperature okay that will give you the maximum relative humidity and vice versa if you want to know what is the minimum relative humidity you can use instead of T air that you can replace with the maximum temperature. So let us come to the adjustment factor. First of all why this adjustment factor is needed? Penman equation as it was developed it was developed for some conditions which are the average conditions. Example these are the major conditions which are used when the penman equation was developed. Radiation is medium to high so it was catering for the conditions when the radiation is between medium and high range. The R h maximum is between medium and high and the daytime and the night time wind conditions are such that the ratio is around 2. So the moderate daytime wind is double the night time wind. So these were the set of conditions which were used and it was found that whenever some of these conditions change the values which are obtained using the Penman equations they vary a lot. The inaccuracies which are incorporated they are quite large. Count for those corrections or to account for the variation in these factors when they are prevalent in the actual area the C factor was devised. This is the table which is recommended by the FAO. This table gives the C factors and if you look at this part it is having the R s in millimetres per day and these are the R s values 3, 6, 9 are different R s the solar radiation values. For R h maximum this is R h maximum this block gives the maximum of 30 percent. This is on this side is the U day in meters per second varies from 0 to 9. Now for these 3 combinations for a given R h maximum for a given R s we have 4 different values then you can interpolate and for given U day this is the wind velocity the daytime wind velocity from 0 to 9 meters per second and another factor which is the unite ratio and in this particular case this belongs to ratio of 4. U day, U night are the wind conditions of day and night their ratio is 4 then this part can be used. So for these 4 combinations you have this part and you can find out what is the value of C. Similarly if the R h maximum changes now here in the next one everything else is same but R s maximum is 60 percent. So the next one is 60 percent the next one the third one is with R h maximum of 90 percent and likewise the other segments are also given where you have the R h maximum is this column 30 percent but here U day unite ratio is 3 in the this block this is R h maximum of 30 percent this block is 60 percent and this block is 90 percent. So you can use this table to find out what are the appropriate conditions in terms of R h maximum in terms of the wind condition the day and night wind ratio wind speed ratio and the R s which is R s on that particular day and the day wind speed this day wind speed is taken at 2 meters height again. So knowing these you can evaluate what is the coefficient C which should be which should be used. Now if you look at this table you will find that whenever the conditions are closer to the ones which have been used when Mn equation was derived for example in this particular case you will find that in all the cases the conditions this particular area is having something closer to 1. This is the R h maximum is 60 percent in this case the height ratio is around 3 if you look at the next one when it is 2 we are still closer to 1 is 0.991.05. So the conditions these C values are very much different they are in this particular case they are even 0.46 when the conditions are that you have the U day the velocity is very high that is 9 and the relative humidity is very the maximum relative humidity is very low so in that case the coefficient or the factor which is almost close to 50 percent that has been used that means you are you are having a value you are getting a value from the Penman equation which is very high so it is over-simulating the conditions and that is why you need a factor to bring it down. So I have seen in detail what are the various ways of calculating the reference drop of upper transpiration there is only one mode method which is a different method which is the Pan evaporation method which if I again bring out the old slide we have covered these 3 methods the 4th method was the Pan evaporation method in which you only needed the evaporation data and the data on the environment that is how the Pan is where the Pan is situated what is the environment closer to the Pan and you can use the data on the humidity and the wind if is available otherwise you can use the estimated data. Let us look at first of all what is what is a Pan this is an instrument is a very simple instrument which is nothing but is a vessel which is a circular vessel and the diameters they are different pans which are available in literature in different countries people are using various types of pans but I am trying to give you one pan which is quite popular is known as US weather bureau, weather service, class A pan is 121 centimetres in diameter the depth is 25.4 centimetres what you do is that you fill this with water up to which you normally fill the water this depth should be maintained in such a way that the fluctuations are within around 5 to 7.5 centimetres from the rim of the go maximum up to around 7.5 centimetres so what you do is that you keep on pouring water regularly the known quantities of water so that you know that what is the depth at that time you keep a record of what was the depth at a particular time of the reading when the reading was taken what was the depth how that depth has been depleting in time that was what will give you that how much is the lost water because of the operation activity then you again to the desired level that means you are within this range and again that process goes on. The requirements are there are some requirements for placing this pan as it should be placed on some platform the they can be a wooden platform so that you are not they can be a wooden platform on which you can place this so that there is lot of air which is passing through and the ground surface temperature is not affecting the temperature of the water but there are different types of pans there are pans which are which are known as sunken pans which are buried inside the ground and there is a pan which is known as the Colorado sunken pan there are pans which are even floated inside the lake so you can you can have it on install on a float what happens is that it depends where you are making the observations suppose if you are making the observation in the lake and you want to know what is the lake evaporation now if the lake is there suppose you have this lake and you have installed the pans over here now this pan this pan will be able to give you a reading which is much different than if you install the same pan on the ground because of the fact that evaporation activity is taking place on the lake then what you are getting here the water vapours which are making this air saturated activity is much different because now you can with the with the novel which you have gained you can see that this air will be very saturated it will be having lot of moisture available at its air mass. In comparison to this air where you have only the water surface in this very small body and the they can be the wind which is regularly replacing this this air mass which is somewhere in this area now with that replacement this air is always the air which is over this particular pan will be much much drier it will be having much more absorption capacity with the result the evaporation which will be taking place from the pan on the ground will be much higher than the pan on the lake surface. So that variation can be there you can you will find that depending on the type of depending on the environment in this case this is what is the environment the environment in this case is different because one is inside the water body the other one is on the land surface. Similarly if there will be a situation where you have some cropped area here this is having the air is coming over the top of some cropped area that will have a its own impact on the the evaporation activity at this place. So all these things will define the environment but what we are looking at right now is that we are the the FAO has assumed that the they will be only considering in question is the U.S. class A pan and using that pan the relationships have been developed. So they have also given some conversion tables that if you have some other pan how you can convert how you can use a factor which will convert the the reading into a equivalent class A pan. This is the expression which is used to get the ET0 reference crop evapotranspiration and is a function of E pan that is the pan the pan reading as a pan evaporation in millimetres per day and it represents the the value over the period which you are considering if you are considering a month then what is the the the evaporation in millimetres per day over the month the average value. And Kp is a pan coefficient which has to be used, this pan coefficient is a function of climate and the pandemic environment. This is a very simple equation as we have in the other cases the only question is that this is what we are absorbing, E pan is what we are absorbing in the observatories or wherever the pan is installed only Kp has to be evaluated which needs some further information. But to incorporate the the environment the environment there are two cases which have been defined one case case A in which the place where the pan is on this case this case deals with that situation where you have the green crop on the windward side in the near immediate vicinity of the or relationships which have been developed to find out what will be the impact of of the green crop that means the extent can vary if this varies what will be the impact so there is one parameter what is the fetch of the green crop which is then followed with the dry surface and the other case is the other possibility if you have the pan installed in a area in which is having the green crop which is much away from the pan location and in the near vicinity in the immediate vicinity the dry surface is available. How much is the extent of the dry surface that is again is a variable which will be taken care of but in both the cases it has to be a certain that the the windward side has to be known and the climate or the environment will be dependent on which is the windward side okay. If the windward side changes your environment might change because what happens the wind direction is what is responsible for knowing whether the the air mass which is coming over the in or which is passing over the pan what is the condition of that air mass because that is what is going to go on the activity of the evaporation. Now having known these then the the Kp has been this particular table is very small and so I will try to explain what are the various variables which have been considered here. Now to find out the Kp value from class A pan that is the condition this is the case for case 1 or case a the various things which are considered here are what is the value of Rh mean in percentage there are 3 cases which are given when Rh mean is low when is medium and when is high so in the case of low is less than 40 percent what would you say 70 percent and greater than 70 percent then we have wind which is expressed in kilometers per day we have conditions which are the light, light wind what rate we had covered these things in the beginning when we had looked at the nomenclature that what are the various ranges when we talk of light, light was less than 175 and this very strong was greater than 700 kilometers per day. Then another parameter which was introduced was the windward, windward side distance of beam crop that is what we were saying that this can be variable so there are 4 different levels when this is around 1 meter to 10 meters 100, 1000. So these values now are the values of Kp for different levels 0.65, 0.7, 0.75 similarly when this is very high it is 0.75, 0.85, 0.85, 0.85 so in between you have the other values now this is what is given in this table that is what this table is about this table gives for case A all these Kp values similarly for case B here all these Kp values for different fetch this is the fetch in the case of case B and again for the load we demand high r h mean value as well as for conditions which are light wind this is this belongs to the light wind conditions this belongs to the moderate wind and the next one strong wind very strong wind. So you can you can use these for finding out what is the value of Kp and once you know the Kp value you can what is the ET0 using the pan equation so with that we have seen all the 4 methods we have seen what are the various data requirements how the method has to be used what are the other assumptions used in using these methods and with that we close this particular section of the topic where we are trying to we were trying to find out the ET0 and we were trying to look at the effect of the climate on the crop water requirements. So we have only seen the first impact what is the impact of the climate on crop water requirements and for that purpose we we tried to define a reference crop which is gas in the present case though there is another crop which is alpha alpha which is also used for the reference crop as reference crop. So it is a material because we said in the beginning that any crop which has which does not vary in its growth much that can be used as reference crop. So in the next class we will start with how we go to incorporate the the effects of the crop characteristics into the crop water requirements how we how we evaluate the crop water requirements that is the the remaining portion we will look into any question.