 Hello everyone, welcome to the next lecture in the course remote sensing principles and applications. We are discussing the topic of passive microwave radiometry. In the last lecture, we discussed topics such as like the atmospheric influence on microwave wavelengths and how antennas used to measure the microwave signals coming from earth surface, but all the different components from the earth surface and atmosphere system that will reach the antenna. All these basic concepts we discussed, today we will continue with those topics. So the last class I told you about real aperture radiometer and synthetic aperture radiometer. And also as example, I have shown you how data is collected by SMAP satellite which is an example for a real aperture radiometer and small satellite which is an example for synthetic aperture radiometer, just like basic introduction I told you. So for this particular lecture, we will not discuss in detail about like how synthetic aperture radiometer works, it is like out of the scope of this course. We will just briefly take a look at the real aperture radiometer and its data collection. So just look, we will just do a quick recap of how SMAP satellite collects data. So as shown in this particular slide, the satellite has like a antenna that is fixed about an axis. This antenna will be rotating continuously along this particular vertical axis. So as the satellite moves like in this particular direction let us assume, the antenna will be keep on rotating like this and it will be continuously collecting data in form of circles. As you can see from here, each as the antenna rotates, it is going to collect like each line like one new line for its every rotation. So it is going to rotate continuously like this. So as it rotates, it is going to collect data along this scanning line every time. So as the satellite moves, the data is going to be collected in this particular fashion. Each line is going to be built like this. So this is like the basic working principle of how the real aperture radiometer works. So now we will get a brief look at the spatial resolution or the JFOV, the footprint of real aperture radiometers. So in general, the JFOV or like the IFOV that is the angle, say each sensor will have or each red element will subtend a small solid angle on the ground. We have seen it. It is the case for optical sensors too. So each sensors will subtend a small solid angle. So based on that particular solid angle or that if we call it as like IFOV, based on IFOV and the orbital height, the sensor will define a footprint what we call it as JFOV. So the angle that is subtended by the sensor element on the ground, the IFOV is basically limited by lambda by L, factor of lambda by L, like here it is limited by antenna beam with what we call as antenna beam with and it can be shown that it is limited by factor lambda by L where lambda is the wavelength in which the micro radiometer is working and L is the length of the antenna. So if we take a look at like a satellite like SMAP. So the antenna has like a 6 meter diameter works in L band. So 1.49 gigahertz or lambda is roughly 21 centimeters at 685 kilometer height. From these data we can calculate. So if we do this lambda by L, we can calculate the angle subtended by the antenna on the ground will be 0.035 radians. So this is like a circular footprint. So you take the orbital height, multiply this angle in order to get the ground coverage. So we can see that so the orbital height multiplied by the angle subtended by the antenna will give us a footprint of roughly 24.2 kilometers. So this is like a minimum value beyond which the JFOV cannot become finer. So actually like the SMAP acquires data around the resolution of around like say 40 kilometers which is much cozier but this is like a minimum limit. So the minimum limit itself is in the order of like 24 kilometers. So one ground or one footprint the satellite covers on the ground will be in the order of tens of kilometers. So this is the general nature of passive microwave radiometers. So passive microwave radiometers they normally tend to have a very coarse spatial resolution because of this lambda by L constraint and also if you look at in a physical sense the energy coming out from the earth surface in a microwave region is very small. Like if you recall the Planck's curve for earth surface let us say this is 300 Kelvin black body curve essentially microwave portion falls in this tail region and the energy emitted by the earth surface is pretty low when compared with this TIR bands. So the energy is very low and we know that for sensor to get some meaningful output it should collect some good amount of signal then only the signal to noise ratio will be high and then only it will be able to differentiate between this is the true signal and this is the noise. So some meaningful amount of signal should be collected. So in order to collect some meaningful amount of signal the sensor should actually have to look at like a very large area. So this is a major limitation of passive microwave radiometers though they are like they provide all weather capability almost and except under like very extreme circumstances. The coarse spatial resolution actually will limit the application of passive microwave radiometry to different fields. So the calculation that we made actually like for the radiometers lambda by L accounting for the 24 kilometers is actually for a nadir looking antenna. But most of the cases real aperture radiometers the antenna may not be nadir looking it may be tilted away from the nadir say for example a SMAP it is tilted roughly by about like say 40 degrees that is if this is like a vertical axis the antenna will be having like a angle away from the nadir. So the antenna will be looking like this it will be like subtending like an angle something like this. So essentially the spatial resolution what we calculated that is lambda by L into H. So this is where H is the orbital height this was the formula we used to roughly calculate the spatial resolution. But since the antenna is looking away from the nadir we also have to account for that particular thing. So the antenna footprint may not be even like having that resolution of 24 kilometers it has to be adjusted for this terms the angle the cos theta terms and cos square theta terms like in which direction it is basically looking. So the radius of this sorry the dimension of this particular footprint in the direction perpendicular to the scan angle say the scan angle is something like this. So in this particular direction the dimension will be lambda H by L cos theta parallel to the cross section like this the dimension will be lambda H by L cos square theta. So this suggests the spatial resolution what we calculated the 24 kilometers itself is a very small number the actual resolution just by this limitation of antenna beam with itself is pretty high will be in the order of say 27, 28 kilometers. So this suggests that the score spatial resolution nature of passive microwave radiometry especially the real aperture radiometers even like if you take the satellite's mass which is like a synthetic aperture radiometer it just it do not rotate and all but still the spatial resolution is much closer. So it will be still again in the order of say 30 plus kilometers each footprint. So as the frequency increases say these two map and mass satellites or L band radiometers as the frequency increases say with moves to say C band or X band or something like that the spatial resolution will improve to some extent because we have this lambda by L term. So as frequency increases lambda will decrease leading to like a finer footprint but again as we all know as the wavelength decreases say it becomes to expand or C band then the atmospheric attenuation may become high and the satellite may not provide us the all weather capability that we normally require from a passive microwave system. So now let us take a look at like a very simple microwave radiometry model. So very simple model means say how the different components of the signals from the earth's surface gets mixed with each other ok. So initially when I told the different components of the signal that is reaching the microwave antenna I told you that there can be direct signal from the ground, there can be surface reflected atmospheric emitted component, there can be atmospheric emitted component and so on. So initially we discussed four different path where first path is direct emission from ground, second path is surface reflected atmospheric emission, third path is direct atmospheric emission and fourth is subsurface emission. So these four paths I told you. So if we combine path 1 and 4 the direct ground and subsurface has one with each other because both of them anyway indicates the signal from ground if that is the case then we will discuss the total signal that is going to reach the antenna or going to move towards the antenna from the ground surface ok. So here we have a land surface with a temperature Tg, ground temperature ok, we have labeled it as Tg, we have the surface as an emissivity of epsilon i where i indicates the polarization of EMR. As I told you the signals emitted by the earth surface will vary with the polarization and the polarization effect is highly noticed in microwave domain. So the emissivity varies with polarization so and hence the signal that is or the radiation emitted by earth surface will vary with polarization. This effect is not we will not care about this polarization effect in optical remote sensing or thermal infrared remote sensing. But in microwave the effect of polarization has to be taken care of because objects earth surface objects have different characteristics in different different polarizations. So here we have to take into account the variation of emissivity with also with respect to polarization also. So the ground temperature and the emissivity. So here essentially we all know that in microwave radiometry we will be interested in measuring the brightness temperature where brightness temperature in microwave radiometry is normally people will think it as a product of surface emissivity and the temperature of that particular surface. So the product of emissivity and the temperature to physical temperature will give us the brightness temperature. So we will think in terms of brightness temperature because as per Rayleigh gene approximation the radiance emitted by the surface is directly proportional to the product of emissivity and temperature. So rest of the terms there will be a constant so this will be the only term that will be varying. So rather than talking in terms of radiance it is easy to talk in terms of brightness temperature in passive microwave radiometry. So we will just look at the look at how objects interact or how objects emit in terms of their brightness temperature. So this is like a ground temperature and the product of its emissivity. So this is the brightness temperature emitted by land surface. We have an atmosphere. So the atmosphere has a temperature of Ts where people call it as sky temperature and it has a it is like giving out a temperature of Ts and the signals or the radiance emitted by the atmosphere will move towards the earth surface and a portion of it will get reflected towards the antenna. So here the surface has a reflectance of rho i and it has an emissivity of epsilon i. So this is related by Kirchhoff's law. So Kirchhoff's law suggests that 1 minus rho is equal to emissivity. So that is in a given polarization and a given wavelength the surface has an emissivity of epsilon i and it also has a reflectance of rho i where i indicates the polarization and this is the relationship between emissivity and reflectance. So the total brightness temperature from this particular land surface that moves towards the atmosphere neglect the effects of atmosphere we are just going to talk about the effect of ground surface. So this is this basically depends on two components. One is the Tg multiplied by emissivity of the surface that is ground temperature multiplied by emissivity of surface, Ts multiplied by reflectance of surface where Ts is the sky temperature. So you can just replace reflectance or emissivity with reflectance in order to get this particular equation. So essentially what this suggests is the total net temperature of this particular surface which comprises of both the surface emission and atmospheric emission is almost like a linear combination of the surface or the ground temperature and the atmospheric temperature that is called the sky temperature. So that holds kind of like a direct relationship between the brightness temperature that is going out and the brightness temperature of individual components. Whereas in passive microwave radiometry sorry not passive microwave radiometry thermal infrared remote sensing we discussed all these in terms of radiance. If you just recall the earlier lectures I was explaining all these components in terms of radiance ok this is the radiance embedded by earth surface this is the radiance coming towards the ground from the atmosphere. So this is the reflected component of radiance all these things we talked in terms of energy terms or radiance terms. Because there the relationship between radiance and temperature emissivity all these things are highly non-linear the original form of Planck's function is what we were using. Here in microwave wavelengths since we can apply this Rallige in approximation which tells us the radiance is directly proportional to the product of emissivity and surface temperature which is the brightness temperature. So it is easy for us to think in terms of temperature itself rather than thinking in terms of radiance and finally converting in terms of temperature. So this is like a very simple explanation or like a very simple model of telling what will be the different components from the ground that will move towards the sensor. But here we have not talked anything about the atmosphere that is in this particular model we just talked about the ground components we have not talked about the temperature of this atmosphere that will directly reach the radiance that will directly reach the antenna because of atmospheric emission and we also assume atmospheric transmissivity is equal to 1 and all these things. So in this explanation we have not included atmospheric effects. So just to show how emissivity or the brightness temperature varies with the incident angle or the polarization we have given like two simple plots we will just have a brief look at it. So the plot on the left side like we will label it as figure 8 figure 8 tells us how the surface reflectance varies with respect to the incidence angle or we can call it as like look angle like in which angle the satellite is looking and the polarization H represents horizontal polarization B represents vertical polarization. So here we can observe that with respect to polarization or with respect to the look angle the reflectance of the surface varies a lot. So the reflectance maybe you can see at very low look angle or incidence angle we can say that the reflectance is pretty low and it suddenly increases all the way to one at very high incidence angle. So this is like the emissivity sorry the reflectance is highly varying. Similarly emissivity which is equal to 1 minus reflectance that will also vary in the same way because these two share a common relationship with each other that will also vary. So just for this particular ground pixel which we assumed had a ground temperature of where the ground temperature Tg if we assume it as 2 75 Kelvin just as an example. So this top horizontal line indicates the ground temperature Tg the true temperature and the brightness temperature recorded you can see how it varies say the dotted line the black dotted line here indicates the vertical polarization and this black solid line indicates the horizontal polarization. So we can observe how the brightness temperature changes with respect to the look angle and the polarization say for example we will take at a 40 degree angle at 40 degree angle at horizontal polarization the temperature is roughly the brightness temperature is roughly about say maybe 240, 245 Kelvin whereas in vertical polarization the temperature is about in the order of say 250 or 255 Kelvin maybe roughly. So this such as that the same surface at a given temperature will produce a completely different brightness temperature when the surface is looked at different angles or at different polarizations and the effect of polarization and look angle on emissivity is pretty strong. So it will vary a lot with respect to the angle in which we look and the polarization in which we observe. So these things has to be taken care of when we try to observe a surface and use that particular brightness temperature for different applications. In the last slide we just looked at how the surface temperature will vary with emissivity of the surface with different look angles here if we take into account like the atmospheric emission also like whatever atmosphere has emitted that will come toward the surface will get reflected by the surface and it will reach. So it has two components right direct emission from the surface and atmospheric emitted component. So if we assume the sky has a temperature of 40 like 40 degree 40 Kelvin. So roughly it is again like a very low temperature only but still sky we can assume it to be having like a very low temperature. So if we assume it this is like the sky component that is being reflected by the surface. So there in the previous slide we have seen the variation of reflectance of the surface with respect to look angle and emissivity sorry the look angle and the polarization. So here if we take that reflectance multiply with the sky temperature we can get what is the effect of the sky component that is going to move towards the antenna. So here also we can see based on the polarization and based on the observation angle the effect of atmosphere or the temperature of the atmosphere that is going to get added up will vary. So this is like the total effect the combined effect of ground temperature like ground pixel T g is equal to 275 Kelvin and the sky temperature T is equal to 40 Kelvin. So if we combine both of them this is how the net signal will look like ok. So that is like this particular equation the one in the box so this particular equation this is the net effect. The net temperature brightness temperature is equal to sky temperature plus emissivity into T g minus T s. So this equation is like the net relationship and this is like the net final value the angle of incidence and the polarization. So this suggests that the brightness temperature observed the measured value of T is strongly dependent on the observation angle the polarization and also the model for atmospheric temperature because normally when we want to disentangle or remove the effect of atmosphere like the antenna will observe like a combined brightness temperature which will have a combined effect of surface and atmosphere. So we need to use some sort of models to or radiative transfer models to calculate the sky temperature or atmospheric temperature to remove the effects and separate it sorry and separate only the effect of this T g. So all these things all the factors has to be taken care of when we try to work with the passive microwave radiometry signals. So just compare this in analogy with the optical remote sensing. In optical remote sensing I told you that objects will look completely different when we change the look angle when the source object sensor geometry changes right same thing will happen here. Here that the source is earth itself so there is no separate external sources involved but by changing the geometry of the instrument by changing the look angle or by changing the polarization we are going to get a different picture of the same object that is there on the ground surface. The resultant brightness temperature what we are going to get will be highly influenced by these directional effects and polarization effects. So this slide again tells us the net effect of the resolution of two different objects within a given J FOV ok. So this is like a one single like footprint of the satellite ok. So here what we are discussing is there is one particular target object with a brightness temperature of T 1 it is surrounded by a background let us say this is like ocean and this is like a small block of ice on the ocean. So the ocean water will be at a different temperature the ice block will be at a different temperature. So the ocean block the background has a brightness temperature of T naught the target let us say the ice has a target temperature of T 1. So these two are brightness temperatures ok. So that is the product of emissivity of that particular object multiplied by its true temperature. Similarly for the target also this is the product of emissivity of that particular object say emissivity of T target determined by its true temperature. So these are brightness temperatures. So the total solid angle subtended by the sensor in one go is this ok. So this is like the total solid angle among which the solid angle subtended by the target is this much a small fraction of it say omega a omega t. So this is like the within that particular solid angle of small fraction of it is occupied by the target and the entire solid angle this outer circle has a mix of the background may be ocean water and the target may be like a ice block. So the net resultant brightness temperature can be simply given by the fraction of the solid angle occupied by the target omega t by omega a multiplied by T 1 where T 1 is the brightness temperature of target. So the target temperature multiplied by what fraction it occupies within the given what to say if we are given solid angle plus the remaining solid angle 1 minus this particular fraction omega t by omega a. So 1 minus of this fraction will give us the remaining portion of the solid angle occupied by the background multiplied by background temperature. So this will be the net brightness temperature that will be reaching the or that will be reflected in the sensor. So just take an analogy with the thermal infrared remote sensing. In thermal infrared remote sensing I told you that the if a pixel has more than one feature that is a mixer pixel then the net resultant temperature radiometric temperature depends on the weighted average of radiances coming out from each object and the net resultant emissivity we have to take into account. So it is like a complex non-linear relationship we discussed it in detail the definition of radiometric temperature for a mixer pixel. Here in this case in passive micro radiometry it is a very straightforward thing. If a pixel has more than one feature we need to know the individual brightness temperature not the true temperature but the brightness temperature because that is what the sensor will basically sense. So each individual object's brightness temperature weighted by their fraction occupied within that particular JFOV the footprint will give us the net resultant brightness temperature for that particular pixel. So it is a pretty straightforward thing. So it is easy for us to resolve ok this is like the total brightness temperature of the pixel if we know the brightness temperature of different pixels we can resolve it. So it is more straight linear addition of brightness temperatures. It is not as complex as how we do in thermal infrared remote sensing. So concept wise it is easy to understand. So the net resultant temperature brightness temperature of a pixel is given by the weighted average of brightness temperature of each and every feature present within this pixel where the weights are given by the fraction of the area occupied by each feature within that particular footprint. So as a summary in this particular lecture we discussed about the spatial resolution of real aperture radiometers. We discussed a very simple model to describe how the brightness temperature from a pixel containing more than one feature will be reflected and also the effect of atmosphere, effect of atmosphere means how the brightness temperature of the ground and the brightness temperature of the atmosphere will add up in reaching the sensor. So with this we end this particular lecture thank you very much.