 the next lecture in the course remote sensing principles and applications. In the last lecture, we discussed in detail about different spectral indices that are available to us with special emphasis to monitoring vegetation. We also noted what all the different ways or different spectral bandwidths in EMR we should come by in order to derive those spectral indices and I also introduced you some simple applications or some simple themes where such indices are being applied. So, from this lecture and next 2-3 lectures, we are going to see in detail about the thermal infrared remote sensing. Before going on to this particular topic, I would like to tell an additional point about the spectral indices that we discussed in the last class. While finishing the last class, I just briefly mentioned about various indices. But we have to be careful when we use such indices obtained from different satellite sensors. That is, for some of our applications, we may be needing to combine data in the last 30 years, 25 years and so on. Our application may be like spanning over very long time interval. Under such circumstances, we will be in a position to gather data from more than one satellite sensors and use it in kind of like a time series. Say for example, first 10 years, I use data from a sensor called AVHRR. The second 10 years, I want to use data from modus. Such kind of scenario may occur. Sensor may go, maybe like taken out from the service and a new sensor might have replaced it. Under such circumstances, we have to switch sensors as our application needs data over a very long time period. Under such circumstances, we should be really careful. That is, we cannot quickly replace or suddenly replace this vegetation index data obtained from one sensor with another sensor. Because the vegetation index that we have used or that we have obtained will depend on sensor characteristics, the spectral bandwidth of the sensor at which wavelength, like what is the central wavelength and the bandwidth, what is the spectral response function of the sensor. All these things will influence the vegetation index. So, mixing data from different sensors is not a straightforward task and we should always be careful when we want to combine data from multiple sensors, especially when we are going to use it in one single time series. So, first one year data from this sensor, second one year data from another sensor. We should not do this. There should be some sort of intercalibration has to be done when data from two different sensors has to be combined and used in one single time series. This is one important point we have to remember. And second point that we have to remember is the spectral indices that we obtained are susceptible to be or they will be influenced by the sensor viewing angle and illumination geometry and also atmospheric effects. Even some indices are capable of reducing the effects of atmosphere, but still some residual of atmospheric effect will always be there. And also the sensor viewing angle, solar illumination geometry, all these things will influence our vegetation index. So, we should always keep these things in mind. When we want to arrive at some really important result or some high impact result using analysis of such vegetation index, we should keep these things in mind. We will we have to try to remove all these effects to the maximum extent possible before we use them. So, these things are important points that we should keep in mind. Then we work with data, especially the spectral indices data obtained from different sensors. Okay, coming to today's lecture. Today we are going to start with the topic of thermal infrared remote sensing. So, what exactly thermal infrared remote sensing is? So, thermal infrared remote sensing deals with measurement of temperature of the surface and using it for various applications. So, we will see what thermal infrared remote sensing is, why is it called so and what are all the different or what are the difficulties we may encounter while processing the data from thermal infrared satellites and maybe few important concepts that we should know. So, let us get introduced to the concept. Before moving on to the concept of thermal infrared remote sensing, I would like to quickly recall the basics of heat conduction methods that we have studied in our high school physics. So, when heat energy has to transfer from one point to another point in space, it can take three different paths conduction, convection and radiation. So, conduction is a process is a heat conduction process in which heat energy will be transferred from point A to point B by physical contact of molecules in the medium. For example, here there is like a stove that is burning and we have a pot of water to be boiled just kept over the stove. So, along this vessel, so this vessel most likely we will use metallic vessels during cooking processes. So, this will be like a good conductor of heat. So, the heat energy supplied from this burning stove will be transferred along the vessel through the physical contact of molecules like this vessel is a solid in which the molecules, the solid molecules will be tightly bounded with each other. So, first the heat energy will reach the molecules at this point where exactly the flame supplies energy to it. Then slowly through this physical contact the heat energy will transfer from molecule to molecule. So, the molecules themselves may not move, but due to this physical contact or closely packed configuration of molecules, heat energy will move from one to the other. This is conduction. So, molecules will not move, but heat will be transferred from one molecule to another. Next is convection. Convection is the process of heat transferring through physical motion of molecules in the medium that is after heating up the vessel the heat energy will move towards the water molecules. So, the water molecules near the bottom of the vessel will first get heated up and as the water molecule gets heated up it will start moving towards the upper surface and cold water from the upper surface will move towards the bottom. So, slowly there will be like a transfer of water molecules from top to bottom and bottom to top and those molecules that are moving from bottom to top will transfer this heat energy to the other parts within that particular vessel. So, here heat energy is transferred by proper movement of molecules within the medium the molecule itself will move taking the heat energy away from one point to another point. The third way of heat transfer is radiation a non-contact way that is if we go near a burning stove we will feel the heat or if we go near like a burning furnace we will feel the heat from certain distance. So, similarly solar radiation reaching the earth surface all these process they need not have any medium heat energy can just transfer from point A to point B that is where we learn to that electromagnetic radiation energy transfers in form of electromagnetic radiation. So, this is a radiation principle even without any medium energy will transfer from one point to another point. So, in thermal infrared remote sensing we are going to concentrate on this particular way of heat transfer the radiation rather than heat transfer I will say energy transfer in a more generic sense. So, radiation way of energy transfer but why I mentioned all these three conduction convection radiation normally when we study about earth and its different processes energy transfer occurs from one part of earth to another part or from one medium of earth to another medium in all these different ways. And later when we discuss about some common applications of this thermal infrared remote sensing we may have to use this conduction convection radiation way of heat transfer. But in this lecture the introductory part of thermal infrared remote sensing we will concentrate on the radiation way of energy transfer from one point to another point. We all know that any object above the temperature of zero Kelvin will emit radiation on its own due to its own internal energy content that we have seen. And that is the major process that drives even like the earth system like sun's energy is like due to its own internal temperature. Sun is emitting energy because of its temperature and that radiation is reaching the earth and that is driving the major processes within the earth surface. So, not only to sun all objects on the earth surface including humans living things non-living things everything will emit energy due to its own temperature and its internal energy content. And it is possible to measure the radiation coming out of this particular object any object and use it to calculate the temperature of that particular object. Say one of the very common example that we see in our everyday life is taking our body temperature using a handled thermometer like a non-contact thermometer. We might have seen in several spots especially during the covid pandemic times people or medical workers will point a non-contact thermometer towards our forehead or near our wrist. So, that is essentially a radiometer which will measure the amount of radiation coming out of our body and using that radiation it will estimate temperature of our body. So, if the temperature is lower than our normal body temperature or equal to the normal condition they will let off or they will ask us to take quarantine measures. So, that is a very good example that we use in our everyday life. Similar concept when applied for earth observation we call it as thermal infrared remote sensing. So, the average temperature of earth surface is around 300 Kelvin we have seen it and most of the objects on the earth surface will have temperatures in the range of say plus or minus 60 degrees from this value say maybe from 250, 260 Kelvin to maybe 330 or 340 Kelvin. Most of the objects will be in this range typically except extreme conditions. So, at these temperature range say 262, 330 or 340 Kelvin average temperature range the emission from the earth surface if we look at like the blackbody radiation curve we have seen in earlier classes the emission from the earth surface will typically peak around 9 to 9.5 micrometers wavelength. For example, like this is like the wavelength this is like the radiant flux density. So, if we use Planck's law to measure this the curve may look something like this where this peak will be something around say 9 to 9.5 micrometer in wavelength and this energy may start something around say 3 to 4 micrometers. So, earth's surface features when they emit radiation it will not be even near the visible range that is like our live examples because of its own temperature the earth's emission will start to occur something around say 3 to 4 micrometers in wavelength and sometimes for hotter surfaces it may be around like the SWR range but not in visible range. So, starting from this SWR range the emission from the earth surface will start to peak and it will reach the peak around this 9 to 9.5 micrometer wavelength and then slowly it will start to fall after it and it will have like a long tail and it will continue. It will it will not reach 0 immediately but it will continue as like a long tail for quite a long wavelength. So, this peak in energy around this 9 to 9.5 micrometer is essentially where we have to measure the radiance and use it for calculate the temperature of the object that is emitting it. So, in general rather than talking about just 9 micrometers we will tell it in kind of like a range 8 to 14 micrometers. So, which is essentially the long wave infrared part of the electromagnetic spectrum. So, any radiance measurement or any radiometric measurement that we do in this 8 to 14 micrometer wavelength range will help us to understand the thermal properties of the object or using that measured radiance we will be able to calculate the temperature of the object. Actually this is the primary reason why remote sensing in this 8 to 14 micrometer wavelength is also known as thermal infrared remote sensing because the remote sensing we are doing helps us to calculate the temperature of the object and also to understand the thermal properties of the object especially in earth surface conditions. In some other planets the thermal conditions will be completely different the black body radiation may be happening at a different temperature or like a different wavelength range. But for earth remote sensing when we observe it in this 8 to 14 micrometer wavelength range that will help us to understand the thermal properties of object and hence the remote sensing we do in this band in the LWIR band is commonly known as thermal infrared remote sensing. So, I told you 8 to 14 micrometer is like the common range for under normal conditions. But under some extreme conditions that is volcanic emissions or very strong large scale forest fires then the emission from such burning features will be occurring in this 3 to 5 micrometer injectors. Let us say this is let us assume it is a black body curve for object at 300 Kelvin. If we want to draw like a same similar curve for an object at say 700 or 800 Kelvin it may look something like this. So, the peak may be occurring in a shorter wavelength energy content may be high this may be for 700 to 800 Kelvin something in that range it may take a different form. So, normally forest fires and volcanic emissions will have very high temperatures and emission from them the radiance from them will be peaking around this 3 to 5 micrometers. So, essentially for normal earth monitoring activities the remote sensing will be done in 8 to 14 micrometer wavelength. But for this monitoring the extreme cases such as forest fire or something monitoring has to be done in lower wavelength in the SWIR range 3 to 5 micrometers. But now we will restrict our discussions to only 8 to 14 micrometers wavelength that is the thermal remote sensing we do under normal conditions. So, even though this 8 to 14 micrometer is like a generic range most of the satellite based thermal sensors use the wavelength of 10.5 to 12.5 micrometers. Because we know the peak wavelength or peak emission of our earth occurs around 9 micrometer to 9.5 micrometer or sometimes 10 micrometer depends on the temperature. But the 9.2 to 10.2 micrometer wavelength has a very strong ozone absorption band which will prohibit us from monitoring the earth and under this particular wavelength. So, basically even though the earth's peak emission occurs in this range 9 to 10 micrometers we will not be able to measure that because of ozone absorption band in the atmosphere. And hence most of the satellites will move towards the longer portion 10 to 11 micrometer range in order to observe various features on the earth surface. And using this measured radiance we will be able to calculate the temperature of earth surface objects and the temperature we calculate is commonly known as land surface temperature. So, now we will get introduced to the concept of a black body. What a black body is when we learnt about the emission from objects we used Planck's law. So, we said if an object is at a given temperature T that particular object will emit a certain amount of radiation at a given wavelength lambda. This relationship is given by the Planck's equation we know how to calculate it and we know the some certain Planck's curve for objects in different different features like what is given in this particular slide. So, here like each curve given here is example of the black body radiation curve for objects at different different temperature. This we have already seen. But Planck's law gives us a maximum limit for the emission to occur that is if an object is at a given temperature T under the restrictions imposed by thermodynamic laws or physical laws an object can emit this much energy that is like a maximum limit. So, using Planck's law whatever we are calculating will define the upper limit of radiation. So, no object will be able to emit more than that at a given temperature at a given wavelength that will be like the emission maximum it can happen. But most of the earth surface features may not be able to emit radiation with that particular level or they will not be in position to radiate energy to the maximum extent as defined by or as allowed by thermodynamic laws. So, in general for most of the earth surface features the emission from them will be less than what has been given by Planck's equation. So, the ratio of these two that is what is the actual radiation coming out of an object at a given temperature T at a given wavelength lambda. So, the actual value divided by the radiation value calculated by Planck's equation and this ratio is known as emissivity. So, in a more common or loosely it is telling emissivity is the efficiency with which objects can radiate energy. For example, let us say let us take this particular example say this object at 2000 Kelvin temperature and at this particular wavelength say around 1.6 micrometers approximately it is emitting radiant emittance of around 40 watt per centimeter square per micrometer. So, this is like a spectral radiance or spectral radiant flux density. So, this value of 40 is like a maximum limit for this particular object at 2000 Kelvin at 1.6 micrometer wavelength. But in reality real life earth surface objects may have radiation less than that let us say it has just 36 watt per meter square instead of 40. So, as defined by Planck's equation the energy that should come at is 40 watt per centimeter square per micrometer. This is like the spectral radiant flux density. But in reality the object is emitting just 36 watt per centimeter square per micrometer of wavelength. So, if we divide this 36 by 40 we will get a value of 0.9 and this is known as the emissivity for that particular object and that particular wavelength that at 1.6 micrometer. We again to be specific I write it as spectral emissivity. So, spectral emissivity or in general emissivity is the ratio of the actual radiant flux density emitted by the object at a given temperature T divided by the radiant flux density defined by Planck's law for the object for a black body at the same temperature. So, this ratio is one of the important property that we should know about all the objects if we want to calculate the temperature of that particular object using remote sensing principles without knowing emissivity we will be making errors in measuring the temperature of objects using thermal infrared remote sensing. Again we will just quickly get recap to the basic class. We have studied this in detail in the earlier lectures. But just as a recap I will tell you the first and foremost primary law that we will normally use is the Planck's law that will tell if an object is at a given temperature T at a given wavelength lambda what will be the radiant flux density that will be coming out from an object. So, this will basically define the spectral radiant flux density at a given wavelength lambda what will be the emission. Integration of Planck's law in the entire EMR range 0 to infinity wavelength will give us the Stephen Boltzmann law sigma T power 4. So, this will give us the total radiant flux density not spectral but total and the peak wavelength of emission for an object at a given temperature T the wavelength at which peak emission occurs is given by Wien's displacement law. So, these 3 laws are basically the fundamental laws that we have seen in detail in the earlier classes but we will use them commonly especially Planck's law we will use very repeatedly in thermal infrared remote sensing and its calculations. So, coming back to emissivity. So, I told like emissivity is like an important property of all objects. So, all objects will have lesser value of emittance as prescribed by Planck's law and one more important thing that I should tell you is objects which emit radiation as defined by Planck's law are commonly known as black bodies that actually I should have told you before itself. So, I told you that this thing the Planck's equation defines the upper limit of the curve and the objects which behave that or which obey that particular law emits with that particular maximum efficiency they are called black bodies and real life objects normally found on the earth surface will not emit radiation as defined by Planck's law they will have lesser equation and the ratio is what is known as a spectral emissivity that we have seen already. So, this is like the general equation that we normally use for calculating the emissivity the actual radiant from object to the radiation of or the radiation as governed by Planck's law. For a given spectral range we can use like we or we can define a broadband emissivity like this something like this say within a given range say between 10.4 to 11.2 micrometers what will be the emissivity means we can integrate these laws or integrate the radiation using this limits. So, here an example is given for the entire range of EMR spectrum from 0 to infinity but if you want to calculate say between 10.4 to 11.2 micrometers what is the spectral emissivity like a band average emissivity means you can do it using this kind of equation. So, the denominator is basically the Planck's equation what is given by Planck's law or Planck's equation and the numerator is given as a numerator indicates the actual radiation coming out from an object. So, such objects are called non-black bodies that is who objects which has emissivity less than 1 are called non-black bodies we will see in detail and those objects which has emissivity is equal to 1 are called black bodies. So, non-black bodies and black bodies. So, in general most of the earth's surface features are non-black bodies they may not be able to emit radiation with a maximum emissivity that is emissivity is equal to 1 they cannot satisfy Planck's law the radiation from the common objects will be always less than 1 and actually under earth's surface conditions strictly speaking no object is a black body even what people use in satellite calibration systems etc are hypothetical in nature like hypothetical black bodies they are close to a black body the emissivity may be around 0.9999 or 9995 something like that very close to 1 but they will never reach 1 okay. So, strictly speaking all earth's surface objects most of them that we encounter in our everyday life are non-black bodies. So, black bodies are the objects which can emit radiation as governed by Planck's law with maximum efficiency emissivity will be equal to 1 for it throughout. So, maybe we will see how objects are classified based on this emissivity little bit in more detail. So, as I said objects which has emissivity is equal to 1 they are known as black bodies. So, for them emissivity will be equal to 1 in all the wavelengths maybe we will see in this particular slide this is wavelength this is emissivity. For a black body emissivity will be a constant and will be equal to 1 throughout whatever the wavelength we measure such objects are called black bodies. There are certain class of objects for which emissivity will be less than 1 but it will be constant throughout under all wavelengths of our discussion. Such objects are called gray bodies that is here like this particular line. The emissivity is less than 1 at the same time it is not varying with wavelength it is a constant line. Such objects are called gray bodies and there are a certain class of objects for which emissivity will vary it will not be a constant it will vary with wavelength and such objects are called selective radiators. An example is given here this line that has like a varying emissivity value with wavelength. So, most of the earth surface features are selective radiators maybe example for like a gray body we can say a calm deep water body without any disturbance. Water body under thermal infrared wavelengths may have emissivity close to 0.98 or 0.99 and so on. But only under thermal infrared that is even that is not like a perfect gray body. Within the wavelength range of this 8 to 14 micrometers water body can be treated as closely to a gray body. But almost for all the earth surface features emissivity will vary with wavelength maybe at 8 to 14 micrometer wavelength they may be like a constant we may think them as like a gray body. But we know that the black body radiation curve does not stop at this particular range it is it has a long tail it even extends up to microwave wavelengths. Under such wavelengths emissivity may vary. So, strictly speaking all the common objects that we know on the earth surface are selective radiators. So, why we need to care about the selective radiators what will happen look at this particular slide given here this dark black line given here is for like a black body emissivity is equal to 1. So, essentially this curve is like a as given by Planck's law and this dark black line is for a gray body that is with a constant emissivity maybe if we know let us say the emissivity is 0.8 then the radiant flux density for this particular object will be 0.8 times as given by Planck's law it is a constant it is very easy to calculate it. But let us take an example for a gray body sorry a selective radiator. For a selective radiator since emissivity varies with wavelength the radiant flux density from that particular object will be keep on varying at certain wavelength it may be very close to 1 at certain wavelength it will be it may be less than 1 and so on. So, at each wavelength the emissivity will be keep on varying and without knowing the emissivity we will not be able to calculate its temperature. So, without knowing the emissivity means most likely we will end up in a under estimated value of temperature unless we know the correct emissivity value and if this emissivity varies with wavelength that complicates our things we must measure the emissivity of object at all possible wavelengths right. So, emissivity is kind of one of the most important concepts to understand in thermal infrared remote sensing and without knowing emissivity we will be underestimating the temperature of objects. So, as a summary in this particular lecture we discussed or we got introduced to the concept of thermal infrared remote sensing why it has got such a name why it is known as thermal remote sensing and we got also got introduced to the concept of spectral emissivity. With this we end this lecture thank you very much.