 relationship between humidity and temperature. To answer this question I think we have to go to a basic relationship because humidity is basically a function of vapor pressure. So we must have a standing, a proper understanding what is the vapor pressure, how it changes the temperature and that is the relationship which is influencing the effect of temperature on humidity as well. There is a relationship between the vapor pressure and temperature and the relationship is named as psychometric curve which looks something like this, if I express this vapor pressure millibar and on this side we have temperature, this relationship this curve is the envelope curve which gives us the saturation vapor pressure but first of all we have to know what is the difference between saturation vapor pressure and vapor pressure. Vapor pressure as is defined is the partial pressure exerted by the vapors at a particular location and that partial pressure is called the vapor pressure. Now if I give you an example if we have an air mass at this location and this air mass let me say that we are having a air mass which is in a controlled environment, this is a vessel which is which is a closed vessel, air mass is in a closed environment and this air mass is at some temperature, this air mass is at some temperature, this temperature is the temperature at which the air mass is temperature T here. Now if you supply more energy if you if you increase the temperature of this air mass by heating it up the temperature of the air mass will go up and with the temperature the absorption capacity of the air mass will also go up. The air mass can absorb more moisture from this water or you can say that this water since you are supplying energy it will be in a position to evaporate some of the moisture from this water and that moisture will be going into the air mass. That will be there will be increasing the vapor pressure of the air mass to which extent this air mass can absorb keep on absorbing more moisture is defined by this psychometric curve. This is the maximum level up to which it can absorb moisture. So as you keep on increasing the temperature the is at a particular temperature there is a corresponding vapor pressure which is known as the saturation vapor pressure. So this vapor pressure is the saturation vapor pressure which is the vapor pressure corresponding to a particular temperature up to which the moisture can be absorbed beyond that if you will try to try to ensure if you will try to heat it up further there is a chance that since in this particular case we are saying that the temperature is being controlled. We are looking at the same temperature if the temperature is controlled you are increasing the vapor pressure of the same air mass at the same temperature up to a level which is corresponding to a saturation vapor pressure. If you change the temperature then at a different temperature the vapor pressure will be the saturation vapor pressure will be different. So air mass can absorb more moisture if the temperature increases but at a particular temperature there is a capacity of the air mass to absorb moisture and that capacity is known as the saturation vapor pressure. So from that angle is an important parameter which needs to be absorbed. Let us look at another aspect of the same thing that now if I am trying to reduce the temperature of the same air mass I reduce the temperature from this level to this level. Now the air mass is having some moisture availability at a particular temperature when I reduce the temperature what will happen? It will the temperature will reduce to an extent that it will reach this level which is the corresponding level at a temperature T2 if this is T1 at a temperature T2 corresponding to that temperature there is a corresponding saturation vapor pressure. So if I try to reduce the temperature beyond this temperature the condensation will take place and that is what is known as dew point temperature. This is the dew point temperature and at this temperature the condensation will take place. This deficit is this deficit between ES and EA. This is called the saturation deficit. The difference between ES and EA this is known as the saturation deficit. This is an important factor which influences the evaporation activity or in other words the evapotranspiration activity as well because evaporation and evapotranspiration they are related. Is that clear? So if you now look at the relative humidity in this context what is the relative humidity? The relative humidity is the ratio of I think we were giving the nomenclature we were calling the saturation vapor pressure as EA and ED was known as the air the actual vapor pressure of the air. The nomenclature has changed I am sorry for that. You can for all practical purposes you can resort to the same nomenclature EA if this is EA and this is ED this is EA as per our previous nomenclature which we have been using. So in the ratio between the actual vapor pressure and the saturation vapor pressure expressed in percentage that is what is the relative humidity. Is that clear? Now another thing which somebody had mentioned and we were trying to I was saying that there are other ways of expressing the function or the graphical representations which have been given in the last lecture. For example in the case of Blanning-Cradle equation we had used for the correction factor we had used ultimately one graphical representation or ways and means by which you can avoid using those graphical relationships. You can instead there are relationships available which can be directly used if you have all the parameters they are absorbed they are known then you can avoid using. So in this particular case there is another form of the Blanning-Cradle equation which is similar earlier I think in this place this we had this was correction factor now in this particular case and this instead of 8.13 it was 8.0. So this is the there is only difference in this particular case your a is a and b they are expressed further in terms of some other parameters. Example a is expressed in the in terms of relative humidity minimum and the sunshine ratio n by n and b is also expressed in terms of relative humidity minimum n by n and ud the wind speed 2 meters high in meters per second. So that is the daytime wind speed. These equations have been formed by using the regression analysis and they can also be used for example in this particular case to find out the value of b either you can use this relationship or table which is provided I have only written first part of the table this table is extended you have the values for ud of 2 meters per second and this goes up to 10 meters per second. So there are 4 more tables of this kind I have not given the full table is the first part where you have the n by n ratio from 0 to 1 the relative humidity minimum is from 0 to 100 and ud 0 meters per second similarly for 2, 4, 6 and so on those tables are available. So you can either use this table to write the value of b and interpolate between if you have value of these parameters in between or you can use directly this relationship and find out. So they are similarly in other situations in other cases in other formalities there are the options available you can use a simpler tableau form or if you want to computerize if you want to use a program computer program you might need equation which is much easier to use and that can be resorted to there is no the values or the results which you get there are quite similar the percentage of error might be within 5 percent. Now we had started in the last class the Penman method and we had said that the Penman method what is the basis behind we had mentioned that it has 2 terms it does the energy balance as well as it includes the aerodynamic term that is why since it has it takes care of both the options or all the influencing factors because the influencing factors are the radiation is one influencing factor the other is the climate in terms of the wind conditions or the humidity level those 2 things the predominance of those 2 things or those 2 2 items can change from place to place to place. So if you have equation which can take care of both these major influencing elements then you can you can certainly come out with the results which are which are quite close to the actuals which are very realistic the errors are minimized. This is the original Penman equation which is almost similar to what the FU has recommended and this this term we are using as weighting factor W this is a ratio between delta plus gamma which is delta is the slope of saturation vapor pressure versus temperature curve at T mean. Now this is the same curve which we have discussed just now the psychometric curve okay, psychometric constant. So this is what makes the W which we have used in our expression which is recommended by W by FU is the same thing only expressed in a different manner. This also has a term G which is the soil heat soil heat flux that soil heat flux is positive if soil is warming otherwise it is negative this this controls what is the the change of or the heat transfer from the soil into the atmosphere or vice versa. And this is the term which is the aerodynamic term which was again it was there in the original Penman equation and this this term this term is nothing but is 1 minus W if you take this is gamma delta divided by delta plus gamma if you take 1 minus delta by delta plus gamma that is what is here. This is the vapor pressure deficit which we have just talked about that is the difference between the saturation vapor pressure vapor pressures at the air temperature. This is the variation which is very slight variation in terms of the difference between the original Penman equation and the modified one and the modification they have only given more emphasis on the C parameter which is the adjustment factor which is to compensate the conditions which have been assumed in the original Penman equation. So there are some situations there are some conditions which are which can be prevalent in some areas which are not the same as have been assumed in the original Penman equation. So those conditions when you take care of those conditions and you apply the correction factor that is done through the correction factor C. Let us try to go through the various elements of this equation and try to look into how we compute those elements how we calculate those elements what are the various relationships available what are the various requirements in terms of the basic data which is needed to compute these different elements of the Penman equation. So we will start one by one the first one is the vapor pressure deficit which is E A minus E D and since we know that this affects the air humidity which in turn affects the ET naught this deficit how to compute this deficit in actual practice there are many ways of doing the same but that to be adopted will be a function of what you have available what type of data is available. Let us look at these different cases which can be possible or which can be used depending on what type of data you have available with you. The first case is when you have the data on maximum temperature minimum temperature the data on maximum relative humidity and the minimum relative humidity these are the various data which are available then you can use a relationship you can find out what is the mean temperature you can find out the mean relative humidity and these are the examples example has been taken where the actual values have been taken just for assumption sake these are the values which have been shown here so that you can better understand the computations. So if you take the mean temperature mean temperature is the mean of these two temperatures the maximum and the minimum temperature that is 28.5 degree centigrade in this particular case and the relative mean humidity the relative humidity here can also be found out by taking the mean of these two values which is 55 percent. The psychometric table or the psychometric curve which I have shown you just now that is also available in the form of a table because it is a unique curve is an envelope curve which is a universal curve that gave you the saturation vapor pressure at any temperature. So this which is the table between the temperatures in degree centigrade and saturation vapor pressure Ea which gives for different temperatures what is the value of Ea is this visible anywhere is not important by this in the sport material which we are giving you will have all these tables available but suppose if this table is not available you can still use this equation can be used there is a relationship between the saturation vapor pressure and the mean temperature and this relationship can be used to get the value of the saturation vapor pressure. This is alternative to using the table but this table is quite a easily available table one can find in any standard resource material or the textbook. Once you find out the saturation vapor pressure then the actual vapor pressure can be found out by using the relationship between the relative humidity and the vapor pressures. The relative humidity is Ed by Ea you know the Ea value you can find out Ed you know the relative humidity I mean the relative humidity you know so Ea can be Ed can be found out Ed is 21.4 millibar in this particular case so you can find out the deficit. There is one situation in which you have these data available and you can find out what is that the saturation vapor pressure deficit. Let us look at an over case where you have the data available on maximum temperature, minimum temperature and the psychometric readings do you know what is psychometer is is an instrument which you use to absorb the wet bulb and the dry bulb temperatures is something like there are different kinds of equipment which are in use but the one which is aspirated means where you are the you can use the ventilation that is the one which is something like a Dattler. You have a Dattler where you have 2 thermometers one is for the the reading of the air, air temperature and the other one is for the wet bulb in which case you are you are taking a porcelain cloth slightly wetted with water and wrap it around the second thermometers bulb okay. So when you do that what happens? It evaporates that moisture which is available in the cloth the damp cloth, evaporation reduces the temperature because of the loss of the latent heat of evaporation okay. So when you lose that temperature how much temperature you will lose will be a function of what is the it will be it will be depending it will be depending on what is the humidity level what is the temperature. So that these 2 temperatures the wet bulb temperature and the dry bulb temperatures these 2 temperatures are from the psychometric readings there are different there are other kind of psychometers also which are not ventilated which are not non ventilated psychometers and that correction can be applied because if you create that ventilation it will have more evaporation if you do not create the ventilation it might have less evaporation because of the fact that the air mass which is immediately closer to that wet bulb which will be after sometime if it is laden with the soil the water vapors then unless that is replaced that air is replaced it would not be in a position to evaporate any further here because you have seen that in the case of air mass the air mass reaches let me give you an example suppose this is the body where the evaporation is taking place so the water vapors they go into the this particular volume of air now this this air mass if it becomes saturated and this is not replaced another air mass which is having less water molecules then the evaporation activity will stop there because this air mass has been totally saturated and you know that at that particular temperature the air mass is not in a position to absorb any more vapors so if you have that is that is how the wind affect the evaporation that is where the wind effect comes into evaporation the wind enhances the air mass which is absorbed with the water vapors to replace that air mass with a fresh air mass which is which might be having much less amount of water vapors if that happens then the evaporation activity will proceed at a very faster rate at a very higher rate otherwise the activity might stop after sometime because of the higher level of humidity okay. So from that angle if we if we have these dry bulb and the wet bulb temperatures available then again you can find out what is the in temperature and you can also find out what is the saturation vapour pressure at that temperature that is using that relationship or using that table you can find out that might not be visible to you if I put it in this if this can be enlarged you might be in a position to see this part this is the table between the vapour pressure dry and wet bulb temperatures now this is the dry bulb temperature here temperature in degree centigrade which is given from 0 40 here on this side is the depression and depression in the wet bulb in degree centigrade what does that mean the difference between the two the difference between the wet bulb the dry bulb and the wet bulb temperature so this goes from 0 to 22 degree centigrade this part of the table is for altitudes between 0 and 1000 meters whereas this part of the table is the same thing but for a different for the altitudes between 1000 and 2000 meters. So you if you know the dry bulb temperature and you also know what is the depression in the wet bulb what is the difference between the two knowing these two and knowing what is the altitude of the location in which at which you are applying this you can read out what is the vapour pressure the actual vapour pressure ed that actual vapour pressure can be directly required using this table and this is for this aspirated psychrometer this table is for that there is a rubber table which is to be used in case you are using a non-mantelated psychrometer there is a similar table which gives the vapour pressure with respect to the bulb temperatures and the wet bulb temperatures for a non-mantelated psychrometer. So knowing these values you can read the ed value the pressure at the temperature and the wet bulb depression in this particular case the difference between the dry bulb and the wet bulb is 4 degree centigrade you are reading the value at dry bulb temperature of 24 degree centigrade with the wet bulb depression of 4 degree centigrade and the value is 20.7 millibars and you can find out the the deficit there is a third case you might not have the data on psychrometric readings available you might not have the relative humidity available but you have instead you have the dew point temperature which is available the data on dew point temperature is available along with the maximum and the minimum temperature. Again the first two parts are the same that you can find out using the main temperature you can find out the saturation vapour pressure but to find out the ed you can do that if your relative humidity of the area is close to 100 percent you must have seen in this case where I was trying to explain the psychrometric curve what happens in the psychrometric curve this is this curve if you know the dew point temperature if this is the dew point temperature and this was the air mass if the relative humidity that level is quite close to 100 percent that is very likely that the two will the dew point temperature and the wet bulb temperature they will be same the dew point temperature will be quite close to the wet bulb temperature and which will be approximately same as the minimum temperature these three quantities these three temperatures provided humidity level relative humidity is close to 100 percent that means you are somewhere in the near vicinity and in this particular case it would not happen because in this particular case if this is by ed it is quite likely because there is lot of deficit is there it is very likely that the relative humidity would not be 100 percent because for the relative humidity 100 percent what is the ed this has to be ed has to be quite close to the ratio of ed and ea has to be close to 1 so that means this deficit will be quite minimum the closers you are if I am somewhere here the two will be quite close the ea and ed they will be quite close is it clear in that situation this this case you can use this only in a situation where you have relative humidity which is close to 100 percent in that situation your minimum temperature the wet bulb temperature and dew point temperature they will be quite they will be quite close to each other and if that is so you can use the psychometric curve to find out what is ed so ed will be ed will be close to the saturation vapor pressure at the dew point ed will be nothing but in that case ed will be nothing but the saturation of pressure at the dew point temperature and once you have that you can find out what is the deficit so these are the various situations which can be utilized to find out the saturation pressure deficit. Next let us look at the wind function which is used in the case of wind function here and this is part of the aerodynamic term that wind function we have already looked at ea minus ed that is the next part which we are trying to look at right now and this particular case the wind function is expressed as this equation as this expression in which capital U is the wind run the 24 hours wind run and kilometers per day 2 meters height in many cases you might find the actual observation of the wind speed which is being done in the field it might not be available at 2 meters height because of various reasons the instrument which is installed it might be installed at the height which is different from this standard 2 meter height which is to be used then for that the correction factor has been recommended you can use this correction factor which is between the environment height and at 2 meters it is 1 if it is less than 2 meters then a correction factor which is more than 1 has to be used if it is more than 2 meters a correction factor which is less than 1 which has to be used which is quite obvious because if you are very close to the surface there will be more resistance the actual wind speed which you are which you are measuring will be much less than the prevailing wind conditions so the correction factor has to be greater than 1 on the contrary if you are going above that then again you might be overestimating the conditions so you have to apply a correction factor accordingly so this is again this is the correction factor which is recommended by F A O for the wind function this is the table which is available which gives the wind function with respect to that formula which we had just written which is this 1 plus u by 100 okay and this is the wind and kilometers per day ranging from 100 to 900 and on this side you have the fractions available if it is 110 you can use this this is from 10 to 90 so if it is between 100 and 200 and is values which are between 0 and 90 you can use this table and you can still interpolate if you have some value which is between 20 and 30 so the 10s and the lower digits can be 10s are given here the lower digits can be interpolated and next is the waiting factor which is this factor is 1 minus w this waiting factor is to incorporate the effect of wind and humidity in the eto and again there is a table which is available which gives the values of the waiting factor 1 minus w this is the temperature from 2 degree centigrade to 40 degree centigrade the altitude is on this side from 0 to 4000 for different altitudes and for different temperatures you can read out the value of the waiting factor 1 minus w similarly the waiting factor w which is the component in the radiation term this waiting factor is also related to the temperature and altitude and this is the replica of the earlier table the same thing but is 1 minus the values of the previous table so it is the same table with a slight modification because the total weightage is 1 what is the weightage given to the radiation term the remaining weightage is given to the aerodynamic term in many situations you might this is very simple if you are using these tables but procedures available there are expressions available where if you have the available data you can use those required data and you can find out the weightages yourself by using the relationships directly instead of going to the tables so if you are again if you are writing a program you are writing a software you might find that these relationships are much easier to model than to use those tables the way we had defined the weightage the weightage factor w this was the delta slope of the saturation vapor pressure and this is given in terms of this equation delta can be directly found out using the mean temperature of the air in degree centigrade and the psychometric constant thing that is the ratio between the vapor pressure deficit and the wet bulb depression it can also be expressed in a simpler form in which this P is the atmospheric pressure in millibars and L is the latent heat of vaporization there are further there are expressions available to find out what is the value of atmospheric pressure and that is given in terms of these variables P0 is the standard sea level atmospheric pressure P0 is the standard sea level temperature and this is in kelvin's delta is the standard lapse rate in kelvin's per meter or is the universal gas constant for air this is 287 joules per kilogram kelvin in G is the acceleration due to gravity E0 is the base elevation in meters and E is the elevation of the location in which you are interested similarly the is an expression for latent heat of vaporization which is a function of the air temperature that can be used to find out if you have a data which is required in this particular case which means the rate on all these variables you can certainly use this expression for finding out the weightage factor yourself otherwise you can is very convenient to use the tables so there is no restriction tables can be used if you feel that the tables are much easier to be used if you are accuracy because in that case you will have to interpolate and in some cases is recommended that the table should be preferably used because all these equations where the regression analysis has been used is the accuracy is not as good as you can get in the case of tables because when you have used the regression analysis the fit the goodness of the fit is another criteria which has to be looked into it depends how many how many data has been used how many different conditions have been incorporated in doing those regression analysis and what was the goodness of it so I think is is just a function of availability if you have the data available you can use either of the things with the slight loss of accuracy but it will be more dependent on where you are using whether you are using in a system or you are doing it manually so that will be will be making the basic difference and I think we can stop here for today any question