 to the next lecture in the course remote sensing principles and applications. We are discussing the topic of thermal infrared remote sensing. In the last lecture, we discussed about the definition of radiometric temperature for a mixed pixel. We spent considerable amount of time in defining how radiometric temperature has to be calculated for mixed pixels. What will be its implications of such a definition? If we want to upscale the data to a coarser resolution that is I want to go from 100 meter resolution to 500 meter or 1000 meter resolution let us say. What will be its implication? How to do it? Such sort of theoretical principles we dealt in detail. In today's lecture, we will move to the topic of retrieval of land surface temperature from single channel thermal data. That is let us take example of Landsat series of satellites. Starting from Landsat 4, Landsat series of satellites had a thermal sensor inbuilt between it thermal infrared sensor to be more specific. So, using that we can calculate land surface temperature. So, now we are going to see how to do it. But our concentration will be primarily on sensors with only one thermal channel mostly. Why not two thermal channels? Let us take example of another sensor called MODIS which is one of the most widely used sensor for several applications. If you take that sensor, it has two thermal channels BAM 3132 and they have an operational LST product currently available. That is as a end user, we need not calculate the land surface temperature from them. Land surface temperature data is already available to us. We can just download and use it for our applications. But if you take Landsat series of satellites at the time of recording this lecture or going through this particular course, there is no operational land surface temperature product available. So, what it means as an end user, they will give us the calibrated DN values. They will give us only the DNs. From the DN, it will be our responsibility to calculate land surface temperature and use it for our applications. So, if we know how to retrieve surface temperature from that particular data, it will be helpful for us and that is what we are going to see in this particular lecture. So, the retrieval of land surface temperature from satellite data is an ill posed problem. What is an ill posed problem? For each band of thermal data, sorry for each band of thermal channel, we can write one equation. Let us say our sensor has two bands of thermal channel for example, I am telling let us say our sensor has two thermal infrared bands. One let it be around 10.4 to 11.5 and the next we around 11.6 to 12.5 micrometers. Let us say two thermal channels are there. This is thermal channel 1, this is thermal channel 2. So, if our sensor has two thermal channels for a given pixel we will have DN in thermal channel band 1 and DN in thermal channel band 2. Using this, we can calculate radiance in thermal channel band 1, radiance in thermal channel band 2. Using these two, we can calculate LST. So, how to calculate LST? Using the same Planck's law. How this thing will vary? The radiance in band 1 is equal to emissivity 1 into Planck's law of wavelength 1, temperature of the pixel t, radiance 2 is equal to emissivity in this particular band 2, Planck's law of band 2 for an object of temperature t. That is here what I am writing is the surface is at a temperature t, the temperature is not going to change. Whatever be the band or whatever be the wavelength we observe, surface is at a true temperature t, that is not going to vary with wavelength. But the radiance that we are going to observe from satellite is going to vary you with respect to different wavelength. Say in tier band 1, the wavelength is 10.4 to 11.5. In band 2, the wavelength or bandwidth is 11.62 to 12.5. So, the bandwidth is different for channel 1 and channel 2 or band 1 and band 2. Hence, the radiance coming out in different wavelengths will be different because Planck's law curve will look something like this. So, if I observe at this wavelength, the radiance is different or if I observe at this wavelength, the radiance is different. Same concept here. I am looking the subject at two different wavelengths, object is at the same temperature t, but just because I am changing my wavelength of observation, the radiance is going to be different. That is point number 1. Point number 2, emissivity also will vary with wavelength. I said emissivity is spectrally variant. So, emissivity is different. Now, look at this equation. Radiance is connected, radiance is equal to emissivity times Planck's function of temperature t are two bands I have written this. Temperature t is same. So, this is one unknown. What I have to calculate? My interest is calculating this temperature t. So, here this is equal, this two temperature are equal in two equations. So, that is one unknown and we have emissivity in lambda 1, another unknown. Similarly, emissivity in wavelength 2, that is another unknown. From satellites, we can calculate radiance in channel 1. Similarly, from satellite we can calculate radiance in channel 2. So, we have two equations, but we have three unknowns. Emissivity in band 1, emissivity in band 2 and temperature of the object itself. So, this is the case of t-air observations. If I have n thermal channels, then I will have n equations and n plus 1 unknowns. That n plus 1 unknowns indicates n emissivities, emissivities in these n thermal channels plus that land surface temperature. So, whatever be the number of bands you have always there will be one more unknown than the number of bands that you have in the sensor. So, if you have only once thermal sensor, like in the case of Landsat satellites, Landsat 4, 5, 6, 7 had only one thermal sensor, only one thermal channel. You will have two unknowns, one emissivity in that band, one land surface temperature. If you have two bands, you will have two emissivities plus one land surface temperature. This is like a recurring problem, it is not going to stop. That is what I said, retrieval of elasticity is an ill posed problem. So, we need to correct the radiance observed to the satellite, both for atmospheric effect and emissivity effect. How to correct for emissivity effect? Somehow we have to bring in emissivity from outside or we need to use some other constraints basically. So, I told you we have n equations and n plus 1 unknowns. So, we should somehow remove any one of the unknowns, like substitute the value to it, remove it out of equations, so that we have n equation and n unknown variables. Or on the other hand, put some constraints on this variable that is okay, this is related to this, this is related to this, like this if we start putting constraints over it, we can reduce the number of unknowns, like this some way we have to resort to and solve this problem. So, normally for sensors with a single thermal infrared channel, we have to calculate emissivity separately. So, normally when we do LST retrieval from Landsat series of satellites, what we will do is we will take the DN from the sensor, convert the DN to radiance, atmospherically correct the radiance to bring it to surface value, independently calculate surface emissivity, combine these two, put it in Planck's function and calculate the surface temperature. This is the general outline of how to calculate Landsat phase temperature from single channel TIR sensor. We will see in detail how these steps are being done. So, the first step let us take or let us look at the atmospheric correction. So, I have already told you in previous lectures that how and all atmosphere will modify the radiance reaching the sensor. We need to correct for it. How to correct for it? Again I have told you some ways when we discussed about atmospheric correction of optical data that is at the time of satellite overpass, observe atmospheric variables, temperature, humidity, pressure, water vapor concentrations, CO2 concentration, etc. Substitute all these values in a radiative transfer models. Simulate how atmosphere will behave, how much emission will be coming out from atmosphere, how much will be atmospheric absorption, all these things you simulate. Use those values for correcting the atmosphere. So, that is schematically given in this particular slide. So, here atmospheric correction of TIR observations can be carried out using radiative transfer models. Some examples of these models are called MOTRAN, RTTOB, etc. These are some of the famous or familiarly used radiative transfer models. So, these radiative transfer models will simulate the radiance reaching the sensor in the observation bandwidth of TIR sensor. So, this will basically simulate, this is the temperature of the surface, this is the radiance coming out of the surface and this is the radiance reaching the satellite. How this radiance has been transformed to this radiance? What are all the components of atmosphere that changed this? That will be simulated by this radiative transfer model. Some of the models are available to us publicly like this RTTOB models and all are we can download and use it without any commercial thing. But sometimes as a end user, we may not have access to such things and we may not have the computational resource to run these models or we may not have the atmospheric data to run these models. So, how to do it as a end user? Is there any simple way to do this? Yes, especially for Landsat series of satellites, there is one simple way to do this. The way to do this is use what is known as an online atmospheric character tool. What exactly is an online atmospheric character tool? In this slide, I am just giving you the output of how that what is a website will work. So, the website address is given here. At the time of this course, recording the address goes something like this, atmcorps.gsfc.nasa.gov. It is basically a website which has links to radiative transfer model RTM plus a atmospheric reanalysis model. So, what this will do is go to this particular website, enter the date and time of your satellite overpass, enter the latitude and longitude over which your satellite image is acquired. Say this is my image, it is acquired over certain portion in India, let us assume. Say over here, let us say it is being captured in the peninsular part of India. So, at what date and time it was acquired, what is the latitude and longitude of the central area of the image we can give from by looking at the image. If you give this, even if you do not have any other information like here this minus 999 represents, I am not given any input to it except for this data. First January 2019, this is the latitude, this is the longitude, this is the GMB time, 5 AM, GMB time in roughly 5 AM means 1030 AM Indian Standard Time. I have given only this data. For this data and for different satellites, Landsat 5, Landsat 7 and Landsat 8, Band 10, this website will simulate the atmospheric variables that we need for our atmospheric correction procedure. This will give us, okay, for this particular satellite at this given lat-long, this will be the output or this is how atmosphere will behave. How this website does? As I said before, the website has in background, has a radiative transfer model and an atmospheric model running behind. As soon as we give the date, time and latitude and longitude from the atmospheric model, it will take all the variables required, feed it as an input to the radiative transfer model, give these things to us output. So, if we are interested in calculation of Landsat's temperature from satellite data, especially Landsat satellite data, this website is of primary use. But just imagine one thing, this is applicable only for Landsat series of satellites. Landsat 5, 7 and 8, that also only Band 10 in Landsat 8, that is one thing. And also this will, this website will give us output for data acquired on or after year 2000. There is like certain date in year 2000, before which this website will not give us any outputs. But Landsat has the data acquired right from say 80s, mid 80s, 1980s. But for that time period, we cannot do atmospheric correction using this particular website. But for data acquired after the year 2000, we can use this. So, that is for the last 20 years or so, it will be possible for us to correct Landsat data using a very simple way. But this is like a very crude procedure, crude procedure in the means, it just takes everything from atmospheric models, we are not giving any live ground observations. So, we have to keep this in mind, this is the best possible atmospheric correction tool available to us. Now, let us assume using this website or using some other way, we have calculated the atmospheric parameters needed for our computations. How to correct for the effect of atmosphere? Just recall the radiance reaching the sensor in thermal band, what we have discussed in earlier lectures. So, the radiance reaching the sensor in thermal band is a combination of direct surface emission, surface reflected, downwelling component of atmosphere plus path radiance. It has three components, we have already seen it. Our actual interest is this, the surface component, what is being emitted by the surface due to its own temperature. We do not need this, path radiance is unwanted term, we also do not want this particular term atmospheric downwelling radiance. So, if you remove this and invert this equation, we will get this particular formula. The land surface temperature Ts or LST whatever we can call is equal to the radiance reaching the sensor minus the path radiance minus this particular term, the surface reflected atmospheric downwelling component divided by emissivity into atmospheric transmissivity. This term is atmospheric transmissivity. We know what transmissivity is, we have defined this or explain this in detail in previous lectures. So, from that website or using the radiative transfer model, we will be getting this term upwelling path radiance, this term downwelling radiance and this term atmospheric transmissivity. So, tau k or atmosphere upwelling and radiance atmosphere downwelling, these three components we will get from that particular website or using the radiative transfer models. So, for a given bandwidth, these three values will be known either using an RTM or using that particular atmospheric correction, online atmospheric correction tool. So, just come back to this equation. Now, we know these three values tau or atmosphere downwelling or atmosphere upwelling, still we do not have this emissivity term. So, atmospheric correction can be easily done using that website for Landsat series of satellite. Next step, we will look at the way how to estimate surface emissivity. So, calculation of surface emissivity will be next step, atmospheric correction somehow we have done using the website or using RTM, radiative transfer models. For calculation of surface emissivity, there are again plenty of methods available, variety of ways are there. For our course, we will not go into detail about explaining all the methods, but we will look at one simple method called the NDVI threshold method. So, NDVI threshold method means it basically assumes any given pixel on the land surface has vegetated or non-vegetated components, most likely non-vegetated component means soil components, let us assume. So, what this method will do is emissivity of vegetation is fairly high, like in the introductory lectures about thermal infrared remote sensing, I showed you some values of emissivity for vegetation, most likely they were about like 0.95 and above, sometimes 0.97, 0.98 such high values. So, emissivity of vegetation is can be considered as constant say 0.97 or 0.98 and emissivity of soil also can be estimated. So, if we can estimate these two things, we can combine them linearly to calculate the emissivity of a pixel. So, in principle or in a simple terms, if a given image is like this, analyze the data or analyze the time series of data and find out, if the NDVI, NDVI is normalized different vegetation index, we have seen what it is earlier classes. If NDVI is less than certain threshold, let us assume this pixel is full of soil. If NDVI is more than a certain threshold, let us say it is more than let us say it is 0.6 or 0.7, then the entire pixel is full of vegetation. If NDVI is lying somewhere between these thresholds, then that pixel is composed of both soil and vegetation. It is a linear mixture. So, how to calculate it? This model will simply assume, if the NDVI is less than NDVI soil, assume soil emissivity to it. If NDVI is more than NDVI of vegetation, assume vegetation emissivity to it. And if NDVI lies in between a threshold, calculate the emissivity linearly. Linearly means, so calculate what is the fraction of vegetation within the pixel. Let us say a single pixel has 40% vegetation and 60% soil. So, 0.4 into emissivity of vegetation plus 0.6 into emissivity of soil plus some cavity term. This is called cavity term. So, this is the simple principle of this NDVI threshold method. So, NDVI vegetation normally we will assume a constant value say 0.98 assumed. Soil emissivity is highly varying. It will vary a lot using depending on various factors. So, for calculating soil emissivity, what we will do is we will develop a relationship relating reflectance in red band with emissivity in thermal band. We can develop certain equations. There are literature showing this particular relationship. So, using the observation in the red band, reflectance in red band and this developed empirical equations, you can calculate soil emissivity. Combining the soil emissivity with vegetation emissivity, you can calculate emissivity of a mixer pixel. Maybe I am not going to explain all the finer details of this method. There are plenty of literature available, but I just wanted to introduce to you a one simple way of estimating emissivity. There are like other different ways of doing it, but when the course develops and it is running, we will see certain helpful literature that will help us to understand this better. But right now what you have to remember is emissivity of a pixel is normally calculated as a linear combination of emissivity of vegetation and emissivity of soil. Emissivity of vegetation is considered more or less a fraction, sorry constant, whereas emissivity of soil is derived from the relationship between or derived from reflectance in red band and combining these things, we can calculate emissivity. This is one of the very simple methods called the NDVI threshold method. In practice, it is easily doable and people are using it to a large extent. Okay, so now let us assume we have emissivity also and we have already atmospherically corrected the data. Now let us go back and look at the previous equation. This is the equation which we described earlier. So, if you look at this equation, the atmospheric terms are already known. Emissivity we can estimate using many different methods. Actually, there are very simple equations also relating NDVI with emissivity. Like most of the single channel methods use NDVI as the primary indicator of surface emissivity because vegetation plays a major role in controlling the emissivity of a pixel. So, using NDVI, somehow we can calculate emissivity. So, we know all the things needed, radians observed at the sensor, all the atmospheric parameters, emissivity has been calculated. If we know everything, we can put it in Planck's function, invert all the values to get the surface temperature. So, this is the simple way of estimating surface temperature from satellite observations. Now, as an example or as a case study, let us see how surface temperature can be estimated from Landsat 7th satellite. So, for Landsat series of satellites, we have what is known as a user's handbook or some user guides will be there. They will give equations something like this. So, some sort of equations will be there like this. If you look at Landsat 7th or Landsat 8th or Landsat 5th, equation will be there, but this constants k1 and k2 will vary. k2 is here, k1 is here. How this equation has been derived? This equation has been actually derived from the real Planck's function. So, this is like the original Planck's function we have seen earlier. So, this is like the radian flux density of Planck's function. Convert this into radiance. So, that is drop this pi, radian flux density divided by pi will give us radiance for Lambertian surfaces or isotropic radiators. So, divided by pi, you get 2 hc square by this equation will be there. Combine all the constants, combine hc, this hc by kt. If you combine all these things, we will finally have a simplified equation like this. The radiance is equal to c1 by lambda power 5 exponential of c2 by lambda t minus 1, where c is given this like this, c2 is given like this. Nothing but we have combined this hc square, this kt and all. So, we have combined several constants to create one simple constants and the units have been changed to micrometer of wavelength. So, this is like a simplified representation of Planck's law, that is it. This is nothing but Planck's law only, but instead of using several constants, we are combining them to create one single constant. Now, using this, so this is like the simplified value of Planck's function. Now, if a satellite sensor wavelength is defined, say for Landsat 7, it observes in this particular range 10.4 to 12.5 micrometer range. So, for these wavelengths and using the spectral response function of the sensor, so using this wavelength and the spectral response function of the sensor, if you integrate this over this wavelength, we will get this equation. So, this equation given in the Landsat user's handbook is nothing but a very simplified version of Planck's equation that is integrated over the wavelength range of Landsat satellites bandwidth, that is all. So, they know the wavelength over which Landsat sensor observes. They know the spectral response function of that particular band. We have already seen what spectral response function is. Just go back to the lectures discussing about spectral resolution or spectral characteristics of a sensor. There, we have discussed in detail about spectral response function. So, here the Planck's function has been inverted, that is instead of calculating radiance from temperature, now we know radiance, we want temperature, just reverse them, reverse this to get inverse Planck's function. In the inverse Planck's function, integrated between the range of whatever the bandwidth of the sensor and we will have one final equation with constants. So, this equation is defined, the constant values are available in Landsat metadata file and also in Landsat user's handbook. So, what we have to do as a end user, download Landsat data from the DN, convert it into radiance. At the time of satellite overpass, using any radiative transfer model or using this atmospheric correction website, calculate the atmospheric parameters, tau r upwelling and r downwelling, correct the satellite observed radiance, independently estimate emissivity, correct the radiance again for emissivity effect. That is essentially what I am asking you to do is apply this equation, that is T s is equal to b inverse of this, where all the terms are atmospheric upwelling, downwelling, transmissivity, emissivity, everything is known. So, this will give you, the term within the bracket will give you what is known as the corrected radiance. The radiance observed by the satellite sensor, corrected for atmospheric effect and surface emissivity effect. Take this corrected radiance value and substitute this in this particular equation. Like if you substitute this corrected equation in this particular equation, k1 and k2 are already defined and it is available from Landsat user's handbook. If we do this, we can calculate the Landsat phase temperature from Landsat series of satellites. So, maybe like when you people find time, try to, you can several online tools are available like Google Earth Engine. They are like open source software is available to download data and use it. Maybe in the later series of lectures, I will just give you a brief introduction about the data sets available from satellite. So, you can try on your own using the simple principles, how to calculate Landsat phase temperature. So, this is the generic procedure of retrieval of Landsat phase temperature from Landsat series of satellites. With this lecture, sorry, we end this lecture with this topic. Thank you very much.