 Hello and welcome to this lecture. So, we are at lecture number 4 which is part of module 1 and in the last lecture we learnt how to mathematically define a wave and then we understood the meaning of few terminologies like radiant flux, radiant flux density, irradiance, emittance, etc followed by radiation laws. So, we discussed about Stefan Boltzmann law which tells us that higher the temperature of the radiator greater will be the total amount of radiation that it emits and we discussed about Wien's displacement law. So far we have not even begun understanding exactly what are microwaves propagating through or how does the medium influence the electromagnetic waves. Because we know that different materials let it be glass or water or wood or concrete. So, different materials tend to react differently to the electromagnetic wave. Transparent materials may bend, refract the light some may be transparent only to a small range of wavelengths. So, in that context let us try to understand about what exactly happens when energy is incident on a black body or a grey body. Now, energy can get reflected, it can get transmitted, it can get absorbed. So, to quantify these to differentiate these let us try to define few parameters which are easy to understand like the reflectivity that is the ratio of power reflected from a surface to the incident power in a given direction. Power reflected from a surface by power incident. Next is absorptivity. Remember I mentioned that incident energy it can either get reflected it can get transmitted or it can get absorbed. So, what are we doing? We are trying to quantify these processes through few parameters. We are trying to define reflectivity which is nothing but the power reflected from a surface by power incident. Absorptivity is the power absorbed by a medium by incident power. Similarly, transmissivity is nothing but the ratio of power transmitted through a medium to the power incident on the surface of a medium. So, we discussed about reflectivity absorptivity transmissivity easy to remember is not it? Now, the conservation of energy implies that all the incident energy is either reflected absorbed or transmitted through the material. This means we can have an expression like this where reflectivity plus transmissivity plus absorptivity is indicated as 1. Now, in remote sensing measurements we assume the objects to be opaque to thermal radiation. So, next let us try to understand how microwaves interact with materials. By materials in particular atmosphere is of interest to us is not it? Because if we are to use satellite data for each observation, we should clearly understand the influence of the intervening atmosphere and we know that atmosphere as such is divided into 5 different layers of which closest to earth is what we have the troposphere which reaches up to 15 kilometers from the surface of the earth and we know that troposphere is thickest at the equator and it is thinner at the poles that is north and south poles and majority of the atmosphere is contained here in the troposphere which includes water vapor, dust, ash, clouds etc. Now, next layer up is stratosphere which extends from top of the troposphere known as tropopause to approximately 50 kilometers altitude and high concentrations of ozone makes up the stratosphere. Again, top of stratosphere is known as stratopause and then we have mesosphere which reaches as far as about 85 kilometers above the earth surface and then we have thermosphere and then the uppermost layer of exosphere. Now, we should be mindful that the active and passive sensors which we have discussed in the previous lectures, they are satellite born and they are high up in the exosphere and they are trying to sense information from exosphere, they are trying to look at the earth surface and try to get the information. So, this diagram is for us to be aware of the distance that a microwave has to travel to make a detectable signal. So, through this section, we also get a justification as to why microwaves are preferred for earth observation, we will see that shortly. Now, a few more terminologies that will help us understand the propagation of microwaves through atmosphere is scattering. I am introducing a few terminologies easy to understand terminologies. Now, scattering is nothing but the redirection of an incident electromagnetic energy by an object. Now, you may ask but then reflection does the same, refraction does the same and diffraction does the same, they all are redirecting energy, is not it? So, shouldn t they be called as scattering then because the purpose is same. The answer is yes, you know they all are considered as different forms of scattering, reflection, refraction and diffraction all are considered as different forms of scattering. So, please make a note of how I am defining scattering, it is the redirection of an incident electromagnetic energy by an object, by a target. Now, reflection is actually ordered scattering from surfaces with features less than the wavelength, diffraction is ordered scattering at discrete boundaries. Now, please note that in scattering what counts as in what is important is the size of the target in relation to the incident wavelength. Let me give you three extreme cases now. Assume the size of the target is much smaller than the wavelength. So, here assume d is a target, the size of target is very much smaller than the wavelength lambda. The scattering that occurs in such a case is known as Rayleigh scattering, Rayleigh scattering which is important when dealing with microwaves scattering in the atmosphere due to water droplets. In Rayleigh scatter as what is written it occurs when the atmospheric molecules and tiny particles are much smaller in diameter than the wavelength of the interacting medium and the effect of scatter is directly proportional to 1 by lambda raised to 4 which means shorter wavelength gets severely affected, yes? Now, as the next extreme case, let us consider something known as my scattering, my scatter. Here I am indicating the diameter of the target d to be almost equal to the wavelength. Herein the scattering is sensitive to small changes in target size or wavelength. So, my scattering. So, the longer wavelengths tend to be more affected by my scattering and water vapour and dust are major causes of my scatter and they tend to influence as I mentioned earlier longer wavelength, right? Now, till now we discussed about Rayleigh scatter and my scatter. Now, let us look at something known as non-selective scattering. This occurs when the target is very much larger than the incident wavelength, target is very much larger than the incident wavelength and this causes scattering of all wavelength with equal efficiency which explains why clouds appear white. So, this also gives the reason for fog and clouds. So, scattering as such is a very important topic to understand in both active as well as passive microwave remote sensing and microwaves can be scattered from the target on to the field of view of the sensor. In active microwave remote sensing, we are interested in the energy that gets back scattered. So, let us try to summarize how different features on the earth surface react to microwaves. Let us start with the example of oceans. When the ocean is calm, the reflectivity of ocean is a function of water temperature and salinity but then sea is rarely calm as water surfaces are affected by wind. So, gust of wind tends to make the water surface rough and rougher the surface, lesser will be the contrast between horizontal and vertical polarization and both emissivity as well as back scatter is going to change with increasing surface roughness. So, active and passive microwave measurements, they give valuable information about the surface roughness and wind speed. Now, moving ahead to precipitation sized particles or hydrometeors. Hydrometeors refer to water particles which are either in the form of liquid or which are frozen, which are either suspended in the atmosphere or are falling through it. So, at a microwave wavelength, precipitation sized drops, they tend to interact very strongly with microwave radiation and this interaction of electromagnetic waves with hydrometeors, they can cause scattering. What is scattering? It is redirection or it can cause absorption which is conversion to mechanical energy and of course, all of this depends on the size of precipitation particles. So, they affect the properties of high microwaves which are say greater than 10 gigahertz. Now, the size of hydrometeors, they vary depending upon the cloud and the precipitation event. For large liquid hydrometeors that is precipitation and all frozen ones, scattering is significant. Say, you as a researcher, you want to model scattering caused by precipitation, then a convenient assumption which is considered often is that individual scatterers are spherical and uniform. I would not get into more details, but just for you to understand that precipitation sized particles, how they interact with microwaves. Moving on to ice and snow. So, in microwave region, the properties of ice are very interesting because you know the dielectric constant, dielectric constant of water when it is in liquid state is extremely high and as soon as it crystallizes into ice, the dielectric constant drops, it falls, it becomes extremely low making it almost like transparent to microwaves which means wet snow will have high dielectric constant than dry snow. And crystals of ice, they exhibit a variety of shapes and modes depending upon the atmospheric temperature and humidity. And generally for microwaves with an increasing frequency, say greater than 60 gigahertz, scattering signatures, they become more pronounced. Moving on to soil. Now, estimating the bulk dielectric properties of soil is not very straightforward. Soils are composed of loose grains of soil, water and air and in remote sensing, it is the overall bulk properties of soils which are relevant and not the microstructure. So, as water gets added to soil, its dielectric constant tends to increase and dry soil shall act as a volume scatterer. Just a few terms so that you are familiar with how microwaves interact, react to different features on the earth surface. Now, coming on to vegetation. So, interaction of microwaves with vegetation is highly complex because leaves they scatter and in a forest, there are leaves of varying length, varying sizes, varying types. And as the wavelengths of microwaves are of the same order as the structural elements of a forest, the scattering can be quite complex. It cannot be straightforward. It has to be quite complex and small wavelength like X band and C band, they shall not penetrate a dense canopy. Why? Because canopy elements are large for these small wavelengths. Let me reiterate. Small wavelengths that like X and C band, they shall not penetrate a dense canopy because the canopy elements are large for these small wavelengths. Whereas microwaves in the L band and in the P band, they are able to penetrate further into the canopy. And as vegetation increases, the contrast between the horizontal and vertical polarization reduces. Now, just I thought to introduce the behavior of microwaves when the surface is rough. Here, assume H is some height deviation from some mean height of the surface. Now, assume that microwaves get reflected from two different levels of a surface which are separated by a standard height deviation say H apart. When H becomes large such that it is similar in scale to wavelength, the reflected waves tend to interfere in an incoherent manner. But for now, I want to introduce the criterion set by Rayleigh for a surface to be considered as smooth is that the phase difference due to H has to be less than one quarter of wavelength. So, corner reflectors, they form a very special type of objects that is worth discussing here. It is based on a simple principle that when an electromagnetic wave hits or its incident on the corner of two flat plates which are joined at 90 degrees as shown here, the incident wave gets reflected directly back along the same path that is the path of the incident wave. They are often used as a ground control point DCP or in calibration and shown here are the corner reflectors at the microwave calval site of 200 meter by 80 meter area which has been set up by the National Remote Sensing Center through Hyderabad. So, more details about these shall we discuss this part of the upcoming lectures. One thing to note is that corner reflectors they shall be seen as bright targets in the radar images just to introduce the terminology corner reflectors. Now, the next question is what happens when microwave strikes a moving target? Shown here is Doppler weather radar caricature and by moving target as I mentioned earlier it may mean ships, it can mean flights, it can mean precipitation laden clouds for a meteorologist. The important point to remember here is that for moving targets it is the relative velocity in the direction between source and target that is what is important and not the absolute speed of the targets. Coming on to mixed targets, see up until now our focus has been on individual targets say soil, ice, precipitation, vegetation but elements on the surface of the earth are composed of all of these in various combinations, is not it? And in an area where cultivation is say paddy we find vegetation over soil and water. So, all these are present in different combinations and earth surface as such exhibits heterogeneity both horizontally as well as vertically. So, if we assume that there is absolutely no interaction between the features in any manner that is if we assume them to be independent then we can simply add the scattering or emission terms from each feature in proportion to the fractional area that they cover. But you know in the case of forest there exists something known as double bound scattering wherein we classify features as layered media just to give you a few examples. So, as part of this lecture till now we understood more about scattering and I give you three extreme cases when the target is much smaller than the wavelength, when the target is larger than the wavelength and when the target and wavelength are of comparable size. And then we understood about Rayleigh scattering, My scattering and non-selective scattering. As I mentioned earlier scattering is an important topic for us to understand an active and passive microwave remote sensing and we tried to summarize how a few different features on the earth surface how they react to microwaves like oceans, vegetation, hydrometeors or precipitation sized particles, ice and so on. And then we discussed about corner reflectors that form a special category of objects because corner reflectors are going to appear as bright targets in radar images. And then we discussed briefly that in real world the targets are going to be mixed targets, it is not going to be soil alone or water alone, it is going to be mixed targets. So, let me hope that you found this lecture useful and wish you a productive learning. Thank you.