 the next lecture in the topic thermal infrared remote sensing. In the last class we got introduced to the concept of thermal infrared remote sensing and also we started discussing about emissivity and its importance in understanding the thermal properties of object. So today we will continue with this particular topic. In the last class we defined spectral emissivity and its importance and based on spectral emissivity how objects can be classified. So what are some important factors that controls the spectral emissivity of objects we will see now. So spectral emissivity is influenced by the colour of the object. Darker objects typically has higher emissivity, chemical composition, the nature, chemical nature of the object, surface roughness like how rough or how smooth the surface is, moisture content, compaction of the object, wavelength of observation. This is important because that is why we repeatedly call emissivity as spectral emissivity. Emissivity varies with wavelength. With the viewing angle whether we are viewing it from nadir or whether we are viewing it from some other angle all these things will influence the emissivity of the object and hence emissivity has a directional property and sometimes the temperature of the object itself will influence the emissivity. But we may not worry much about this because for the normal temperature range we are seeing this may not be a major factor. But all these other factors colour, surface roughness, moisture content etc will change it. Say for example, if you compare like a dry soil under wet soil like after a rainfall or something. So after like when it rains over like dry soil it gets wet. So when it is dry it will have certain emissivity value. After it got wet the emissivity most likely would have increased if other conditions remain normal emissivity would have increased most likely. But this is applicable only in the thermal infrared range. In other wavelengths this relationship may not be valid emissivity may also decrease especially in microwave wavelengths. But in this particular thermal infrared wavelengths 8 to 14 micrometers for dry soil emissivity will be low. For wet soil emissivity will be high and similarly we also know that when we add water to soil when the soil get moist its reflectance goes down. We have already seen this the reflectance property of soil. So the reflectance decreases. So emissivity will increase. So normally it will appear dark and its emissivity will be high. So the colour, composition, moisture, surface roughness all these things will affect emissivity. So these are some of the common factors. So again in order to emphasis the importance of emissivity I have given like two examples here. So this is like a black body curve that is as given by Planck's equation the dark black line and this dotted gray line is for water at the same temperature 350 Kelvin. But water has emissivity less than 1 and as I told you at the wavelengths of that we are discussing like in the infrared range and all we can assume water to be of like a gray body and hence the emissivity can be treated more or less constant. So it will the radiation from water body will be 98% than what is given by Planck's equation. On the other hand let us consider a material called geonite it is a mineral. It has like it is a what to say selective radiator and its emissivity will be keep on varying. So at certain value or at a given wavelength we have to know the emissivity in order to properly change this Planck's equation value to the actual value emitted by it. Either we should measure this and we should bring it there in order to calculate it. So we should know the emissivity values. So what will be the typical emissivity values of real life objects in the wavelength that we are talking about that was between this 8 to 14 micrometers wavelength. The wavelength or the emissivity of most of the earth surface features will is fairly high above like 0.85 or above 0.9. Maybe we will look at this particular chart given in the slide. Say after this 8 micrometer even like we can start at 10 micrometers because as I said most of the earth observing satellites typically measures between 10 to 12 micrometers. So if you look here and if I draw something like this and if I project it here then we can observe that after like between this 10 to 12 micrometer range under where most of the thermal satellites observe the earth surface the emissivity of most of the commonly occurring earth surface features snow, sea water, ice, leaf, grass, etc. typically is fairly high above 0.9 range. So this is like more or less a general property of earth surface objects. In thermal infrared wavelengths 8 to 14 micrometers wavelength emissivity will be like pretty high and the values also will not vary very widely. Say maybe in the later part of lectures when we discuss about passive microwave remote sensing we will see that at such wavelengths at microwave wavelengths emissivity varies very widely. But in thermal infrared wavelengths emissivity variation is not as high as in that particular wavelength it is fairly high like above 0.9 and mostly it will lie in that particular range say 0.85 to 1 or 0.9 to 1 for most of the naturally occurring earth surface features like soil, vegetation, water and so on. So the emissivity of some commonly occurring objects on the earth surface is given in this slide. So under this 8 to 14 micrometer range of wavelength the emissivity of various factors like distilled water has extremely high emissivity, normal water occurring in our water bodies has emissivity of say 0.92 to 0.98, concrete has pretty low emissivity range like pretty low emissivity value. If you look at like vegetation say here you can all observe forest all these vegetation related thing has fairly high emissivity 0.95 or 0.96 and above. Whereas if you look at like metals all these things aluminum, stainless steel, polished metals etc all these things have very low emissivity values. So normally metals which are good conductors of heat and which can reflect a lot normally metal surfaces can reflect lot of energy such objects will have low emissivity. And almost all naturally occurring surfaces like soil, vegetation, water all has emissivity above 0.9 this is like a under normal conditions even human skin has very high emissivity. Snow has pretty low emissivity in this particular band so we have to take care of it if someone wants to observe snow. So now we have seen or we have got introduced to the concept of emissivity and the typical range of emissivity that we can expect in thermal infrared wavelengths or long wave infrared wavelengths. One important law that we should remember in remote sensing or thermal remote sensing especially is known as Kirchhoff's law. What Kirchhoff's law says Kirchhoff's law relates reflectance of an object with the emissivity of the object. So we all we know that whenever some object is kind of emitting or basically interacting with EMR three different processes can occur. Reflectance or reflection, absorption and transmission like let us say this is like some any earth surface feature. When some EMR is incident over it it can reflect a part of it or it can absorb a part of it or it can allow a portion of EMR to transmit to pass through it. These three things will happen. Let us say absorption like first we will talk about this. If an object is a good absorber then it will be a good emitter like if we talk in this particular range 8 to 14 micrometer thermal infrared wavelengths. If an object absorbs well then theoretically speaking it should also emit well because we have learned in thermodynamics that all objects on the earth surface try to be in thermal equilibrium with its surroundings. Normally when you bring a hot body and a cold body near each other it will try to the hot body will transmit radiation or heat energy to the cold body they will try to become like one single equilibrium. Same thing is common for almost all naturally occurring objects. So if an object is a very good absorber like it is absorbing lot of energy then its temperature will be keep on rising right absorbing means taking in more energy. So if it wants to come to thermal equilibrium with its surroundings it also has to emit equally good then only it will emit radiation like it will be absorbing in one end it may be emitting from the other end such that it remains or it moves towards thermal equilibrium with its surroundings. So naturally all commonly found earth surface features if they absorb well they will also emit well. So absorption and emittance we can replace one with each other that is say in terms of like thermal infrared remote sensing we are dealing with emission of objects how much energy objects are emitting. So for our purposes we change this equation reflectance plus transmittance plus absorptance this is equal to one this this equation we have seen already in earlier classes. Now we replace this absorptance with emittance. So reflectance plus transmittance plus emittance equal to 1 because we all know that absorptance is equal to emittance that is our major assumption. And then again look at like commonly occurring earth surface features like sand vegetation etc most likely they will have zero transmittance to thermal infrared thermal infrared wavelengths they may not allow the thermal infrared radiation to pass through them either they may absorb it or reflect it or something okay. So naturally transmittance also will be zero under this wavelengths. So at 8 to 14 micrometer range this equation reduces to reflectance plus emittance is equal to 1 that means reflectance is equal to 1 minus emittance or emittance is equal to 1 minus reflectance. So this is what is given by Kirchhoff's law. So Kirchhoff's law basically tells us that good absorbers are good emitters that is why we have replaced absorptance with emittance first thing and second thing is good reflectors are poor emitters. So if an object reflects a lot of energy in this range 8 to 14 micrometer normally like there is no incoming radiation from sun in this 8 to 14 micrometer range. So if somehow let us say there is like some surface on the earth we are illuminating with some energy source that is radiating at this 8 to 14 micrometer range okay but even like atmosphere atmosphere also emits energy in that wavelength only. So if some energy is falling on an object at this 8 to 14 micrometer wavelength and if an object the land surface object if it is capable of reflecting a major portion of it then according to Kirchhoff's law that particular object will be a poor emitter. On the other hand if that object that is under this influence of this incoming radiation if it absorbs a major portion of it then it will be a very good emitter. So higher the reflectance lower will be the emissivity and vice versa. So this relationship we will quite often use reflectance is equal to 1 minus emissivity when we deal with data processing especially in thermal infrared remote sensing okay. We will now try to understand few or different definitions existing for temperature. Temperature is like a very common word but we can define it in several ways especially when we deal with remote sensing. So one of the commonly used definition of temperature is what is known as a thermodynamic temperature. So what exactly is thermodynamic temperature like loosely putting it or like commonly putting it let us say if you want to measure temperature of an object what we will normally do take a thermometer put the thermometer in contact with the object wait for few seconds take the thermometer out make a reading out of it we will measure the temperature of the object. So how this thing is happening basically we are taking the thermometer and we are bringing the thermometer in physical contact with the object of our interest let us say in olden days how doctors used to measure our body's temperature they will take a mercury thermometer put it underneath our tongue they will ask us to open our mouth put it below our tongue. So they are bringing a thermometer and making it or bringing it in physical contact with object of our interest that is our body. After coming into a contact they will wait for some time why are they waiting for some time they are allowing the time in order to bring our body and the thermometer to reach like a same temperature level that is they want the thermometer and our body to in thermal equilibrium. So the time they allow that few seconds of time they allow during that time our body's temperature will influence thermometer temperature and vice versa and both of them will come toward like one same temperature at that level and then they will take it out they will read a value. Hence thermodynamic temperature can be thought of or can be defined as the temperature which we can measure directly with the thermometer in physical contact with the object of interest and also there the object of our interest and the thermometer should come to like thermal equilibrium and then we measure the temperature of the object. So the temperature we measure in that particular way is known as thermodynamic temperature. So here that is what the definition is given a slide. So this definition is taken from one of the seminal papers by Becker and Lee in the year 1995. So it is defined for a medium in thermal equilibrium. So I said they will leave some time for the object or that is our body and thermometer to come to physical thermal equilibrium and it can be measured directly by a thermometer. So this is the common way of measuring temperature but there we are actually making an assumption. What is the assumption? The doctor is putting the thermometer underneath our tongue and doctor is taking a reading. Doctors assume our body's average temperature all across is very close to or equal to the temperature they measure underneath the tongue. That is the assumption they do but it need not be the case the temperature underneath the tongue may be that but it may change at different points of our body. It will change but that is the most representative measurement the doctors can make. Similarly if you take analogy of some commonly occurring earth surface features if you put thermometer over it measure temperature we are assuming that object is in thermal equilibrium and that particular object is homogeneous. Let us say there is like a water tank. Someone asks us to measure the temperature of water in the tank. What we will do if we take a thermometer and measure just at one particular point within the water tank it may not be representative. The temperature at different points of the tank may vary. Normally what we will do we will take at least some 4 or 5 different measurements we will take average out of it and present it. So what this means the measurement of this particular thermodynamic temperature also assumes the object is homogeneous and isothermal. Isothermal means it is in temperature is not changing it is in equilibrium with its surroundings it is homogeneous in nature. Under such circumstances only the point measurements that we make will be reliable but under normal conditions this may not be valid. Say in this water body example I just showed you I said even within a small tank of water body the temperature may change from point A to point B and also if we measure the temperature at different different depths temperature may change all these things will come into picture. So definition of thermodynamic principle is very simple. You take a thermometer put it in contact with the object of interest let they come to thermal equilibrium take temperature definition is simple but in practice or in reality measurement of thermodynamic temperature is a difficult task because most of the commonly occurring earth surface features they will not be in thermal equilibrium the temperature will be keep on changing they are not isothermal say even if you take like a small water pond you need to take multiple measurements at different different points you will get different temperatures. So these non-homogeneity and non-izothermal nature of earth surface features makes it difficult for us to measure thermodynamic temperature for our various application. Let us say you want to measure temperature of like whole city for some applications we will not be in a position to measure the temperature of each and every point in the city right it is like impossible. So definition of thermodynamic temperature is possible very simple but in reality measuring it is extremely difficult due to the very high level of in homogeneity or non-homogeneity of objects objects are non-homogeneous temperature will change at different different points for the same object and also objects will not be in isothermal conditions isothermal conditions means let us say take a land surface during daytime solar radiation will be keep on like illuminating the surface surface will be getting heated up it will be under like constant process of getting heated up similarly during like night times surface will be continuously cooling down. So it will never be in like isothermal conditions either it will be heating up or it will be cooling down. So the temperature will be either raising or falling continuously. So finding a proper commonly occurring so finding a proper earth surface feature under isothermal and homogenous conditions is bit difficult and hence measurement of thermodynamic temperature is also difficult. The next definition is radiometric temperature. So this is what we are going to measure in remote sensing. So what exactly radiometric temperature is let us say this is like a land surface here we have our sensor. So land surface has a temperature let us say this is like Ts surface temperature and it is radiating some energy this is the radiance. So this will reach the sensor also we have our own atmosphere. So atmosphere has its own temperature T, Ta it will emit radiation towards the earth surface it will be reflected back towards the sensor. So this is the surface reflected atmospheric downwelling radiance. We have seen this already in earlier lectures. So these two terms actually carry the signal above the earth surface features. So the temperature based on the temperature there will be a radiance and similarly based on the reflectance of an object there will be a radiance. So these two paths will carry the signal above the surface. So if you take the radiance reaching the sensor let us neglect all other effects of atmosphere. So the radiance reaching the sensor is practically what is emitted by the object of interest itself and what is emitted by atmosphere. So this is atmospheric emitted term and 1 minus emissivity this is basically the reflectance. So here what is being reflected? So this term is reflection or reflectance of atmospheric emitted component. This is the surface emitted component. So the surface emitted component is equal to emissivity time the Planck's equation. So the emissivity is to correct for how well an object can radiate. So emissivity into Planck's law will give us the actual radiation emitted by the object at a given temperature Ts and this rho times radiance of atmosphere will tell us the surface reflected downwelling radiance terms. So you just kind of neglect this I want to get this Ts surface temperature. So what I should do the Ts surface temperature is equal to observed radiance divided by emissivity of the object when you give this value to the inverse Planck's function then we will get the temperature T. So what exactly inverse Planck's function is? Say Planck's function will tell if an object is at a given temperature T the object will emit a certain amount of radiation at a given wavelength. You reverse it now I observe radiance from remote sensing and using this radiance I know the wavelength in which I am observing and I know the emissivity of an object. So if I know the radiance if I observe the radiance if I know the emissivity and if I know the wavelength of our observation I will be able to substitute all these values in Planck's equation and calculate the temperature of the surface. So this way of measuring the surface temperature that is by observing radiance by knowing the emissivity and calculating temperature this way is known as measurement of radiometric temperature the temperature you are measuring in this way is known as radiometric temperature. So that is again given here in this particular slide. So the radiometric temperature under normal conditions will be the radiance observed by the satellite r lambda minus the surface reflected atmospheric emitted terms. There is also like a path radiance term we have seen it but here we are neglecting it. We assume it has already been removed. So purely speaking the radiance emitted by the surface object you correct for emissivity effect that is you divided by emissivity and then you invert it in plan invert the Planck's function to get the surface temperature and this is known as radiometric temperature. So this radiometric temperature and thermodynamic definition of temperature that we have earlier seen they will be equal only for homogeneous objects under isothermal conditions. Let us say we have like a water body and let us say like the satellite is observing like a small part of water body. So this is like 1 J FOV. So it is observing only that water body continuously. So if the entire pixel is occupied by water body let us assume the water body has a homogeneous temperature and somehow it is in thermal equilibrium. Let us say its temperature is not changing thermal equilibrium at isothermal conditions. Under such circumstances only the temperature we measure from remote sensing the radiometric temperature will be equal to the true thermodynamic temperature that you measure with a thermometer. So this is like a very stringent conditions. So under normal conditions the radiometric temperature that we measure from satellites will not be equal to the physical temperature of the objects on the earth's surface. Because as we have seen most of the objects are they are not homogeneous and they will not be under isothermal conditions and hence these two temperatures the radiometric temperature that we measure from a distance and the what to say thermodynamic temperature that we measure with a thermometer most of the conditions they will not be equal they will be equal only for homogeneous and isothermal surfaces. The next definition of temperature that we are going to see is brightness temperature. What exactly is brightness temperature? Let us say we have a satellite in space it is measuring the land surface it is observing the thermal radiance coming out of the earth's surface it has measured some value okay some L lambda value it has observed. Now if someone wants to calculate temperature they can just take the value put that value in Planck's equation because the wavelength is fixed a satellite once we send a satellite we know in which wavelength it will work. So take the radiance substitute that in Planck's equation invert it to get the temperature that is known as a black body sorry that is known as a brightness temperature sorry. So what exactly brightness temperature is brightness temperature of an object or the brightness temperature is defined as the temperature a black body would have in order to produce the same level of radiance as observed at the satellite sensor. Say I have a satellite sensor up in space some radiance L lambda it is measuring I just take the L lambda substitute this in Planck's equation invert it and I get a temperature. So this temperature is essentially a black body temperature because Planck's law is defined for black bodies. So brightness temperature is defined as that particular temperature that is the temperature a black body will have in order to emit the same amount of radiance observed at the satellite sensor. So this is known as a brightness temperature. We compare this definition with real world objects a satellite is in high up in space land surface is emitting energy it is passing through the atmosphere and my sensor is measuring radiance in order for me to calculate brightness temperature what I do I just take this radiance value substitute this in Planck's equation get a temperature out of it that is it I have not done any correction. So this temperature what I calculated just from mere satellite observation is actually not corrected for surface emissivity effect and atmospheric effect and also the sensor response function I already told you within a given wavelength within a given bandwidth the sensor may not have uniform response at certain each bandwidth or each each interval of wavelength the sensor may have a different response right we have already seen it when we define the concept of spectral resolution. So please go back to previous lectures about spectral resolution we have discussed this what a spectral response function of sensor is. So essentially when we calculate brightness temperature we just take the radiance from satellite put it in Planck's equation and invert it that is all we are not doing any correction. So the surface emissivity effect atmospheric effect and sensor spectral response effect all these things will be there when you calculate brightness temperature. So brightness temperature is kind of like a first hand information I can get just from radiance I am calculating the temperature we do not bother much about what effect atmosphere made how much surface emissivity or spectral emissivity object has all these things we do not care about. So this is another way of measurement but for most of the applications especially in the thermal infrared domain in the 8 to 14 micrometer wavelength normally we would not stop at brightness temperature we will we will correct it for effect of surface emissivity we will correct it for the effect of atmosphere and then we will convert it into radiometric temperature the definition we have already seen and then we will use it. So in today's lecture as a summary we have seen few examples or few ranges of emissivity of commonly occurring earth surface features and also we have defined 3 different temperatures thermodynamic temperature, radiometric temperature and brightness temperature. Thermodynamic temperature is the physical temperature you measure with the help of a thermometer and the object for which you are measuring the temperature we assume the object is isothermal and in thermal equilibrium. Second thing is radiometric temperature that is if there is an object I measure the radiance out of it from the radiance knowing the emissivity value of an object if I estimate the temperature that is known as brightness temperature sorry that is known as the radiometric temperature brightness temperature is a temperature of a black body that will produce the same amount of radiance as observed by a satellite sensor. So essentially the sensor when it absorbs the radiance in it will not be corrected for surface emissivity effect will not be corrected for surface or the atmospheric effects. So brightness temperature is roughly speaking temperature uncorrected for atmosphere and emissivity effect whereas radiometric temperature is if the brightness temperature after doing all the corrections emissivity atmosphere sensor response all these corrections after we do it the temperature we are going to get is radiometric temperature. So brightness temperature and radiometric temperature are kind of related okay so if we whether we do atmosphere correction whether we do emissivity correction all these things will tell us with this we end this lecture thank you very much.