 to the next lecture in the topic thermal infrared remote sensing. Till last lecture we got introduced to the concepts such as what thermal infrared remote sensing is, what a blackbody is, what is meant by emissivity of an object and so on. And particularly in the last lecture we discussed various definitions of temperatures that is we saw what is known as thermodynamic temperature that is the temperature we will measure with the thermometer in physical contact with the object of our interest. Then we saw what is known as a radiometric temperature. So, radiometric temperature is from the object some sort of radiance will be coming out. Observing that radiance and knowing the emissivity of the object if we retrieve the temperature of object that will be known as radiometric temperature. And this thermodynamic temperature and radiometric temperature will be the same or will be equal for objects that are homogeneous and isothermal in nature. Then we also define what is known as a brightness temperature. So, brightness temperature means say some radiance is reaching the satellite sensor using that radiance if we substitute that radiance in the inverse plants function and if we calculate the temperature obtained from that particular radiance that is known as brightness temperature. So, the brightness temperature is essentially the temperature a blackbody will have in order to produce the same radiance that is being observed by the satellite sensor. So, if you compute brightness temperature then effectively we are not correcting that particular temperature for emissivity effect and atmospheric effect. Because when the radiance is travelling towards the sensor in space the surface emissivity will play a major role in defining what energy is being emitted and also it will be further modified by the atmosphere while the radiation passes through it. So, these two things effects or effects of these two things will be there in a radiance that is reaching the sensor and while computing brightness temperature what we do we simply take this radiance substitute the value in plan inverse plants function and calculate a corresponding blackbody temperature. That is why I said brightness temperature means you can think it of as an uncorrected temperature or temperature that is not being corrected for surface emissivity and atmospheric effects. So, today we are going to look at the concept or discuss the complex nature of TIR observations TIR stands for thermal infrared. So, what is the complex nature of TIR observations? So, let us take one particular land area a sensor is looking over it. Most naturally a sensor will not look only at one particular object say we all know that whenever a sensor is seeing a ground it will have like a small area defined on the ground right. We call it as the GI FOV the ground projector instantaneous field of view the aerial extent which is seen by the sensor in one go or in a given instant of time. Within the GI FOV there can be more than one surface feature present there can be a crop land there can be trees there can be buildings water bodies and so on. So, all these things will have their own temperature may be a water body may be little cooler a building may be warmer and so on. So, each object within that will have its own temperature similarly each object will have its own thermal emissivity. So, these two things combined together will impact or will affect the total radiance that is reaching the sensor. So, the final temperature or the final radiance that is going to reach the sensor is effectively the average of all these things average means let us like take an example. Let us say we have one GA FOV here. So, this is one GA FOV. So, there can be many different objects present each object will have its own emissivity will have its own temperature. So, because of its temperature and emissivity all will have its own radiance that is say this is object A the radiance L from object A is given by emissivity times the Planck's function of that particular temperature. So, here TA I will write. So, this is object A I write it as TA. So, what is Planck's function? Sorry this is multiplication 2 h c square by lambda power 5 1 by exponential of h c by lambda k t minus 1. So, this will be the radiance from one particular object say object A. Similarly, there will be there can be n objects within a given GA FOV or within a single solid angle subtended by the sensor like a sensor sees one particular solid angle covering a small ground area. There can be n different surface elements there each having its own radiance with that can be computed using emissivity and Planck's function. And each have its own small aerial extent fraction right say a building might have occupied 2 percent of the GA FOV a water body might have occupied 15 percent of the GA FOV and so on. So, based on how much area they are covering within that single look of the satellite all the radiance will be averaged together and the sensor will see a averaged radiance of all these features. So, within the GA FOV the sensor is not going to see any one particular object it is going to see the radiance that is resulting due to the presence of many different features. Each object will have its own radiance everything will be kind of averaging themselves to recorded to get recorded in a sensor. Now, as a user what we will do as a user this radiance will be converted into dn stored in a satellite image. We will get the dn convert it into radiance using that radiance we will calculate the temperature of the object again. I will explain how to calculate temperature objects some simple steps in the coming slides, but let us assume from this radiance we are calculating the temperature. So, now essentially what we have we have this t rad calculated from satellite as a user this is what we will have in our hand. At the time of image acquisition there were like many different objects each having its own physical temperature t1, t2, t and so on. So, these 3 things will be everything will be different they may be very different or they may be like varying a little, but in essence the temperature of each and every object will be different from what is seen by the satellite. And this satellite based temperature since it is coming from several objects strictly speaking we call it as ensemble directional radiometric surface temperature. So, just imagine this radiometric surface temperature is we know the simple temperature we calculate from satellite. What is this ensemble and directional? An ensemble is the radiance recorded by the satellite and the temperature calculated out of that particular radiance is not due to any one particular feature on the ground it is going to be a mixture or it is going to be like an average radiance of all the features contained within this GAFOV and the temperature computed out of that particular radiance will be actually different from what to say each and every individual objects basically that is why we call it as an ensemble it is a mixture of several things. And it is also directional means the sensor might be looking the ground like this like at nadir sometimes the sensor may be looking something like this away from the nadir and so on. And we already have seen to a sufficient extent that objects will have different different reflectances when we look from different direction. Same way emissivity also will differ when we look from different direction because reflectance is equal to 1 minus emissivity we know reflectant differs in different directions. Same concept will apply to emissivity also. So, objects will emit differently in different different directions. So, the radiance say if a sensor sees a land patch from this particular direction and another sensor see the same land patch but in this particular direction the land patch essentially is one and the same but the temperature or the radiometric temperature recorded by these two sensors is going to be different because of the variation in look angle variation emissivity effect and so on. That is why strictly speaking the surface temperature that we calculate from satellites should be known as an ensemble directional radiometric surface temperature. This is one thing and one more important fact that I should emphasize is let us look at this particular slide for an ensemble of black bodies at different temperature there is not an equivalent black body with a given temperature yielding the same radiance at all wavelengths. So, this may look confusing in the first go but if you try to understand the particular meaning of this what does it mean? Let us say we have like for sake of simplicity let us assume we have two black bodies within a one particular GAE phobia for very simple sake I am telling a given area is occupied only with black bodies that to only two black bodies or let us even start with just one black body for example say one big area has only one black body a satellite temperature or satellite is observing it. We go and measure the physical temperature using a thermometer satellite measure the radiance out of a black body using the radiance we can calculate the temperature back they will match because it is a homogeneous pixel it is a black body everything will match. Let us say now two black bodies are present and two black bodies are at different different temperatures due to the variation in temperature what will happen say black body A will emit differently let us say black body A has higher temperature. So, black body A will emit higher energy black body B will emit lower energy and what a sensor will see it will see a average energy kind of thing. Using that average energy if you calculate a temperature out of it then that particular temperature and the average temperature of these black bodies they will not match that is what the sentence suggests this sentence says for a ensemble or for a mixture of black bodies at different temperature it is almost impossible to have an equivalent black body at any given temperature T to produce the same radiance let us two black bodies are there their average radiance will be something it will be impossible for you to find another black body which will yield the same radiance at some temperature at all wavelengths. Maybe we will get this concept clarified with respect to one or using an example like here the same example what I described in the last slide is given a land surface is like this or some areas like this it has two objects black body one black body two each has occupying 0.5 like half of the area within this particular JFOV. So, black body one is at temperature of 293 Kelvin black body two is at a temperature of 323 Kelvin. Let us say some thermal sensor is observing this and for the sake of simplicity and just for mere explanation purposes here I am assuming the sensor is not actually like a thermal sensor it is a sensor that can sense radiation in entire wavelength range 0 to infinity wavelength that is impossible to have but just for the sake of simplified example I am taking this that is the black bodies will emit radiation in many different wavelengths it will emit we all know that. So, what I am doing I am like creating a hypothetical sensor which will observe in all wavelengths from 0 to infinity as extremely broadband sensor that is now observing this particular what to say particular features of or the two objects the JFOV composed of two objects. Now, let us see what happens basically now in this case what will be the average physical temperature of this particular JFOV half of the area is occupied by a black body at 293 Kelvin half of the area is occupied by another black body at 323 Kelvin. So, the average temperature like the true physical temperature of this particular entire area will be half of average of 293 and 323 which gives you 308 Kelvin. So, if we physically take a thermometer measure at many different points within this area and calculate an average out of it most likely we will end up with this value 308 Kelvin. So, this is the average physical temperature. Now, let us compute this using remote sensing principles as I told you for the sake of explanation I am going to observe this area using an extreme broadband sensor which can observe in wavelengths of 0 to infinity. So, we all know that Planck's function essentially we will use Planck's function for calculating radiance when we integrate Planck's function to 0 to infinity what we will get we will get the Stephen Boltzmann law like in initial classes I have told you. So, Stephen Boltzmann law are now just because I have defined an extremely broadband sensor for this example I am using Stephen Boltzmann law Stephen Boltzmann law is very easy to compute and show on screen rather than computing all the steps of Planck's law. Planck's function is little mathematically has more steps to solve just for saving time I am using Stephen Boltzmann law here, but this is not true for always just for explanation sake I am doing it. So, sigma t power 4 the Stephen Boltzmann law. So, there is two black bodies. So, sigma t 1 power 4 plus sigma t 2 power 4 by 2. So, if you take the radiance emitted by an object will be 517.517 watt per meter square. So, this is the radiant flux density. So, now if I use this if I divided by pi if I do if I convert this into radiance and if I substitute it back to this particular equation then the radiometric temperature that we will be getting will be 309.09 that is sigma t power 4 if I substitute what to say r is equal to sigma t power 4. So, if I use this particular value to calculate this particular t average the t average will be 309.09 Kelvin. So, here you can see for this mixture of two black bodies the temperature we got from remote sensing observation is 309 Kelvin roughly because Stephen Boltzmann law normally we should not apply, but for explanation sake I am telling. Average actual physical temperature is 308 Kelvin. Difference may be just 1 Kelvin, but in real world here we have assumed actually in this example we have assumed two just two objects that to two black bodies. In real world a single GIFOV will have n number of features that can be 10, 15, 20 different features each having own temperature and own emissivity everything will be averaged together to produce one single temperature value and the single temperature value that we are observing from satellite will be different from temperature of these individual objects what we will be getting from satellite will be a kind of a mixture that is why we call it as an ensemble directional temperature. It will be like a mixed signals coming out from all the different objects. So, it will be very difficult for us to calculate the temperature of any one object contained within the GIFOV unless that object is clearly visible it will be very difficult for us to calculate. So, that is the concept. So, the normal or the thermal infrared measurements that we make from satellites are indeed complex measurement complex in the sense like it has a mixture of signals emanating from various objects which will prevent us from calculating the temperature of each and every individual object. The final temperature that we are sensing will be complete can be different not completely, but it will be different to some extent from the temperature of the different objects contained within this particular GIFOV when the satellite observation was made. Now, slowly we will move on to further concepts of land surface temperature, how to retrieve it and all before that we will see one example of how land surface temperature image will look that is given in this particular slide. So, here we have an LST image LST is land surface temperature or otherwise known as surface radiometric temperature that is like the technical term radiometric temperature. So, this shows the temperature map of a small portion on South India. So, this is like the Kabini reservoir, this is the Kabini river and all. So, this is like Kaveri river going like this. So, what essentially it shows then this is like mountain show, this is like Karnataka Kerala, this is Karnataka portion, this is Tamil Nadu, this is Kerala. So, a mixture of three states this is like the Veshingar mountain and so on. What it generally shows look at the color bar the dark brown color here indicates temperature around like 280 Kelvin, yellowish color lighter colors brighter colors indicate higher temperature here for this map it is 327 Kelvin. So, this tells us if you look at this area we can clearly sense it is a river it is actually Kabini river that is flowing and using the water people do lot of irrigated agriculture near its banks. So, these portions near the river channel or actually water bodies or crop lands that are like irrigated using the water from this river and hence they are at a lower temperature. Similarly, look at this mountain portions again the elevation is high these portion western guards contain lot of trees vegetation and so on their temperatures again lower. Look at the central patch these are mostly agriculture dominated areas, but at the time of this image acquisition they were like more or less bare or fallow in age fallow land and hence not much of vegetation is present that is why they have a higher temperature. So, what this generally means if the surface is bare dry without moisture and so on the temperature will be higher for it. On the other hand like here I am meaning the radiometric temperature what we are sensing it. On the other hand if you observe this LST over well vegetated areas or over water occupied areas naturally the temperature of it will be lower. So, using this temperature we will be able to understand the energy processes occurring at the surface we call it as the surface energy balance equation which tells us how the energy coming in at the land gets divided into different components using that we will be able to calculate how much water is lost to the atmosphere through the process of evapotranspiration. We can estimate soil moisture we can estimate vegetation health lot of different applications are there maybe few applications we will get introduced to towards the end of this course. But the general application of the radiometric temperatures it will help us to understand what are the different energy processes occurring at the earth surface. Just two slides before I explained you the concept of ensemble directional radiometric temperature. Now we call a pixel if a pixel or if a JFOV of a satellite sensor has more than one object present within it we call it as a mixed pixel that is that particular pixel is having more than one feature. For such mixed pixels how to define this radiometric temperature or for practical purposes if we want to define and use radiometric temperature for such pixels how to do this we will quickly see this in the coming slides. Here we assume a mixed pixel that is a single JFOV which has several features present within object 1, object 2, object 3 and so on. It has n homogeneous element each element is homogeneous for simplicity I am assuming say this is like let us say this is a water body that particular water body is at a uniform temperature throughout okay. So similarly there are like n different elements and all of them are homogeneous individually at a different different temperatures. So a satellite will be in order to see this particular JFOV a satellite will be subtending a small solid angle omega within this particular solid angle this JFOV will be defined. So this is the JFOV and this is like the solid angle omega. So what essentially we are going to do with this if a pixel has more than one feature then how to define the radiometric surface temperature observed by that particular sensor without going into the detailed explanation and derivation for the want of time I directly move to the last portion of this explanation and I will explain using this two particular equation. Now again I just go back to the JFOV example. Let us say we have three different objects homogeneous objects object 1, object 2, object 3. Let us assume within this particular JFOV or within the particular total solid angle subtended by the sensor, object 1 occupies a fraction of let us say 0.25, object 2 let us say it occupies a fraction of 0.25, object 3 it occupies a fraction of 0.5. That is within this particular single JFOV seen by the satellite three different homogeneous objects are there each occupies a given fraction of area. For simplicity sake I have taken 0.25, 0.25 and 0.5. Let us assume each object has emissivity of emissivity 1, emissivity 2, emissivity 3. Then the ensemble emissivity of this particular JFOV is given by the aerially weighted fraction or the aerially weighted value of emissivity of this all the elements present within it. That is the ensemble emissivity at a given wavelength lambda is given by fraction of object 1 multiplied by emissivity 1 plus fraction of object 2 multiplied by emissivity 2 plus aerial fraction of object 3 multiplied by emissivity 3. This will give the aerially averaged emissivity for this particular JFOV because when we compute land surface temperature when we estimate lands surface temperature normally what we will do we will compute pixel by pixel one pixel we will take the radiance out because we cannot go finer than a pixel in a remote sensing image whatever radiance got stored in a pixel we will take it. So, we have to work with kind of like an average emissivity. So, the average emissivity can be defined like this that is what we are seeing. So, the average emissivity is given by this and the radiometric temperature is given by this particular equation that is the total radiance or the total temperature given by the observed by the satellite is given by each object will have its own radiance right. So, let us say for an object 1 let us assume the radiance is emissivity 1 into l 1 where l or let us say b 1 b 1 is the flanks function emissivity 2 into b t 2 emissivity 3 into b t 3 where here b indicates flanks function t 1 t 2 t 3 indicates the actual temperature of the 3 objects this is the radiance from 3 objects. So, the average radiance reaching the sensor is 0.25 into l 1 plus 0.25 into l 2 plus 0.5 into l 3 radiance from object 1 into 0.25 radiance of object 2 into 0.25 radiance of object 3 into 0.5 because that is the aerial fraction occupied by it and the radiance of each object is given by emissivity times the flanks function at a given temperature t and lambda that is all. So, this is the L average now to calculate the radiometric temperature what we will do the temperature of this particular pixel will be is equal to this average radiance divided by average emissivity if you take inverse flanks function out of it we will get temperature of that particular pixel t. So, it is it may look confusing in the first go, but concept wise it is really simple concept wise what we should do emissivity I think by now it should be clear. Emissivity for a mixer pixel is defined as average aerially weighted average of aerially weighted average of emissivity of different features present within a pixel very easy. To calculate temperature what we should do is we should first calculate the radiance coming out from each and every object average out all the radiances using the fraction like using the aerially weighted average of all the radiances compute an average radiance for that particular pixel using this average radiance and using this average emissivity I have calculated substitute everything in plants function invert it get a temperature out of it and that temperature will give you the ensemble directional radiometric temperature for this particular mixer pixel. So, here the one concept we have to remember is when satellite is seeing a mixer pixel a pixel containing more than one feature the radiance coming out of all the features will be averaged out and the satellite will be seeing a kind of like a average radiance similarly the emissivity will also be averaged out. So, when we calculate the final temperature for that whole pixel we need to use this average temperature average radiance and this average emissivity to calculate the temperature of that particular pixel. So, the radiometric temperature for a mixer pixel has to be computer like this. In literature there are different definitions of this mixer pixel emissivity and so on, but we are we will follow this particular simple definition given in one of the seminal papers. So, this one thing you always have to remember how to calculate the temperature of mixer pixel normally what we tend to do is if a object has let us say let us take the same example three features it is very natural for us to think okay this is object one having certain radiance. Let me calculate radiometric temperature T1 here there is object two let me calculate radiometric temperature T2 and so on. Find out the temperature of this average it out that is let us say let us go back to the same example this is at T1 this is at T2 this is at T3 emissivity 1 emissivity 2 emissivity 3 it is very easy for us to compute the radiometric temperature of this particular pixel using inverse Planck's function that is I am computing temperature for each and every element and if I average them out so this average will be different from what we compute using this particular formula that is temperature in the TIR domain is not linearly averageable you cannot linearly average surface temperature if you have more than one feature present within a pixel or if you want to upscale your image. So, if at all you want to average out temperatures say 10 different objects are there in a given area if you want to calculate the average temperature of that whole area means you cannot average the temperature of all these 10 objects what the satellite effectively sees will be different from this particular average in order to properly compute this you have to follow a very long procedure calculate the average emissivity calculate the average radiance use that in Planck's function and invert it ok. So, the real application may be there in one example which I will show in the next slide here in this particular example I am giving you one problem how to spatially upscale or average TIR data that is let us say you have one satellite image at 100 meter by 100 meter resolution. Now, I want to convert this so each pixel is 100 meter by 100 meter you have surface temperature now I have to compute or make this data to 500 meter by 500 meter for my application I need data at 500 meter by 500 meter how to do this it is very natural for us to think ok. So, within a 500 meter by 500 meter pixel there will be 2500 by 100 meter pixels it is. So, just average the temperature value recorded in each of this 25 pixel that is it very simple right that is what we normally think but we should not do that we should not just take the temperature and average them out it may give us a wrong result technically what we should do is from the temperature or from the original D and recorded in the pixel we have to calculate the radiance of each pixel similarly we have to calculate the emissivity of each pixel average the emissivity out in order to get an average emissivity for all the 25 pixels average the radiance of all these 25 pixels using this average radiance and using this average emissivity substitute this in inverse Planck's function that is this is how Planck's function will be. So, substitute this so substitute this average radiance here so this will be average radiance here emissivity will come here. So, this will be average emissivity take this substitute this average values invert this equation to calculate the temperature T. So, this is how we have to calculate the or we have to upscale the satellite data. So, if you want to change the resolution especially the surface temperature data we have to work like this we cannot directly average a temperature simply we can do that but the results may be erroneous most likely it will be erroneous. So, it is always better to be safe rather than being sorry. So, the major aim of telling you or explaining you all this concept is temperature estimation in TR domain is a non-linear process they will not linearly average their temperature will not linearly add up the Planck's function is highly non-linear. So, whenever we want to calculate temperature for several objects combined together we cannot average them out we have to use this roundabout procedure to do this. So, with this we end this particular lecture. Thank you very much.