 microwave remote sensing in hydrology and are they useful. So as you can see on the screen as part of this module, we will learn the fundamental principles of passive microwave remote sensing and what is a forward model, what is emissivity and the principles of measuring ocean salinity, ocean winds, sea surface temperature and we will also try to understand how passive radiometers can help us in measuring precipitation and soil moisture. Through a few case studies, in addition in this module we shall also cover what is forward problem over land and what is passive polarimetry. All right. So with this background, let us start with our first lecture of module 5. Passive microwave remote sensing, it is very similar in concept to thermal remote sensing. The schematic is shown here wherein the naturally emitted electromagnetic energy in the microwave region are sensed by a sensor that is operating in the microwave region. Remember in one of the earlier slides, one of the earlier lectures, I had asked you to think of a camera without flash, conceptually very similar to what a passive microwave remote sensing is. So let us re-itrate. Imagine a downward viewing passive space-borne radiometer. So this downward viewing space-borne passive radiometer shall be built to sense the upwelling electromagnetic energy from the surface of the earth which reaches the top of atmosphere after attenuation. So I am introducing two terms here that is new to you. Number one is radiometer and number two is attenuation. What you see here on the x-axis wavelength is shown and the y-axis atmospheric opacity is shown. So you can find out the regions of wavelength within the electromagnetic spectrum wherein the atmosphere is more or less opaque. So we can clearly understand why microwaves have the ability to see through clouds. Now the earth surface does emit energy in the microwave region of the electromagnetic spectrum for useful measurements to be taken either from an aircraft or from a satellite. Now let me show you an image here. You know when you see this image on your screen, you can relate it to the ones you see in news channels sometimes when discussing about weather. So shown here is an image from INSAT 3D which is developed by the Indian Space Research Organization captured in 10.8 mu meter infrared region. You can see at the top IMG TIR is given 10.8 mu meter. One can observe that clouds are seen as white whereas if you look at images captured in a microwave region of the electromagnetic spectrum the microwaves have the ability to penetrate through clouds which means you get to see the vertical profile of storms of cyclones and microwave region as you saw earlier it falls within the atmospheric window. It has cloud penetration power. So before I move forward if you are more interested to know about INSAT 3D please make it a point to visit the ISRO website. It is used for meteorological and search and rescue services and it has a 6 channel multispectral imager and a 19 channel sounder. The third new term that I am introducing as part of this lecture is sounder. We will see about radiometer attenuation and sounder soon. So before we start to learn in detail about passive microwave remote sensing just a quick background about what is a black body. In one of the earlier lectures pertaining to module 1 we discussed that black body is a theoretical ideal emitter which transforms the heat energy into radiant energy at the maximum rate that is consistent with the laws of thermodynamics. Now let me simplify the terminology black body it is an ideal body which absorbs all the incident electromagnetic radiation at all wavelengths black body. If it were a perfect emitter is the example of a theoretical ideal black body. Spectral existence can be plotted with respect to different wavelengths. I have taken a point not to include the values of wavelengths or the values of spectral existence so that you get the idea that for lower wavelengths the curves are going to peak. So the spectral existence curves for black bodies at different temperatures are shown here. Same curve but now I have specified the x and y axis. If you notice closely x axis the wavelengths in mu meter are given 0.1, 0.2, 0.5 and so on up to 100 mu meter and on the y axis you can see the spectral radiant existence. Remember try to recollect what we discussed in the earlier modules spectral radiant existence with the unit watts per meter square per mu meter. So the spectral existence curves are shown here for black bodies at different temperatures 300 Kelvin here what you see it has the black body radiation curve at the earth's temperature okay black body radiation curve at the earth's temperature let me write it down 6000 Kelvin shows the black body radiation curve at the sun's temperature let me write it down sun's temperature. Instruments to detect the terrestrial radiant existence operate in the spectral region between 3 to 14 mu meter 3 to 14 mu meter earth's emittance you can see it peaks at 9.7 mu meter and hence the satellite born thermal sensors they operate normally in this range that is 10.5 to 12.5 mu meter spectral region okay. You may be thinking that why am I discussing about thermal sensors in a course related to microwave remote sensing. So this discussion is just to let you know that terrestrial black body curve peaks in the infrared region and not in a microwave region okay but even then there is sufficient energy that is getting emitted from the earth's surface in the microwave region for meaningful for useful measurements to be made from a sensor on board an aircraft or a satellite okay. So with this background let me hope that you remember the radiation laws which were discussed earlier. Let us have a quick recap here we discussed about Stefan Boltzmann law which gives the total spectral existence of a black body at temperature T we discussed about the Wien's displacement law which gives the dominant wavelength at which maximum spectral radiant existence occurs dominant wavelength here in this module we will try to learn about one more radiation law known as Planck's law okay. Now assuming we have a source of radiation that behaves like a black body then Planck's law provides the spectral radiance as a function of both wavelength lambda and frequency. Frequency form you know it is more commonly used in discussions pertaining to microwave remote sensing but then we will switch back to the wavelength form soon but for now let me present the Planck's law here wherein h defines the Planck's constant bt is nothing but the Planck function k is the Boltzmann constants c the speed of light and the frequency is also given at longer wavelengths what happens is kt is going to be greater than h nu which means we can expand the term that is present in the denominator here. So let us try to expand the term in the denominator so I am going to write exponential of h nu by kt minus 1 let us expand it and write it as 1 plus h nu by kt plus 1 by 2 factorial into h nu by kt square plus and so on minus 1 and this can be written as h nu by kt why because at longer wavelengths kt is greater than h nu that is why we can expand the exponential in the denominator and from the expression here I have expanded and then estimated that it is nearly equal to h nu by kt which means I can rewrite the Planck's law. So let us try to rewrite I can write 2h nu cube by c square into kt by h nu which again can be written like 2 kt nu square by c square which in turn can be written like 2 kt by lambda square. What you see here is known as the Rayleigh Jean's approximation. Let me write it down for clarity Rayleigh Jean's approximation. So what did we do? We tried to understand about Planck's law and then now about Rayleigh Jean's approximation passive microwave remote sensing. There are a few key terminologies which it will be better if we discuss about the same. So before moving forward let us discuss about what is emissivity. Shown here in the screen in front of you is the expression for calculating emissivity but in simpler terms it tells us how efficiently a body radiates energy at a frequency in compared to black body. So let me reiterate emissivity is nothing but how efficiently a body is radiating energy at a frequency in comparison with a black body which is why the expression reads emissivity equal to brightness of an object at a temperature T by brightness of a black body at a temperature T emissivity. If you remember the lectures in the earlier part pertaining to module 1 we discussed about the basics of electromagnetic waves, isn't it? But then we had not dealt deeper about what they are propagating through, isn't it? See different materials they can have different effects on the electromagnetic radiation. There can be materials which are transparent, materials which are opaque. If we discuss about light, glass and water they seem transparent. They can bend or refract the light and materials like wood are opaque to light. Here we need to understand about the propagation of microwaves through the atmosphere, the medium being the atmosphere and the wavelength region which is the microwave region. So shown here just to explain the concept of interaction of microwaves through a medium. You see the box that is present which denotes a medium having an extinction coefficient of 0.45 and a refraction index of 1.5. Just to visually get an idea that waves they are comprised of electric and magnetic fields oscillating in mutually perpendicular directions. They change when the medium properties change. Now let me try to introduce you to three terms especially to characterize the electromagnetic properties of a material. One is electric permittivity, second is magnetic permittivity and third is electric conductivity. And when we speak about remote sensing of these terms electric permittivity is most relevant. So let me write it down. Electric permittivity, electric permittivity. So a polished metal surface assume a corner reflector, a polished metal surface it can totally reflect an electromagnetic wave. And we already know, we already have an understanding that electromagnetic waves consists of an electric and magnetic fields which are mutually oscillating perpendicular to one another which means it is that much more important for us to understand about electric permittivity of an electromagnetic wave which has an electric field. Now what if the material is conducting? Say the material you are dealing with is not a corner reflector, it is not a polished metal surface but it is a conducting material, highly conducting material. Then the electromagnetic waves cannot propagate, is not it? Now let us talk about earth's atmosphere because in passive microwave remote sensing we are more interested to learn about the naturally emitting electromagnetic radiation that is emanating from the earth's surface and which is traveling all the way through the atmosphere to register a signal at a sensor that can be either onboard an aircraft or onboard a satellite. So when it comes to earth's atmosphere it is non-magnetic, non-magnetic and most of the objects on earth have a relative permeability close to one. See most of the materials in remote sensing they are not conducting in nature, non-conducting in nature and such materials are called as dielectric. And sometimes you know in textbooks you will find that electric permittivity is used analogous you know in conjunction with dielectric constant. So in this module we will learn about radiometry as well which is nothing but a field of science related to measurement of incoherent electromagnetic radiation. Know that according to thermodynamic principles all materials let it be gases, let it be liquids or solids all materials they tend to emit and absorb incoherent electromagnetic energy. And the magnitude of this thermal emission can be expressed through a relation as shown here which is nothing but emissivity multiplied by Planck's blackbody function. By approximating the thermal emission from Planck function using Rayleigh-Jeans formula the microwave brightness temperature can be conveniently expressed as a linear function of physical temperature and emissivity. So I hope you get the idea of how we started from a Planck's law used the Rayleigh-Jeans approximation and we are conveniently expressing the microwave brightness temperature which is abbreviated as TB. So we are expressing it as a linear function of physical temperature of the body and emissivity. Now emissivity here it is a complex function of dielectric constant whose values are well known for gases and calm water but then the value of emissivity is not so well known not so well defined in the case of rough water and land surfaces. So at this point let me introduce the forward model to you. You see a schematic in your screen we will discuss about that. See a downward viewing airborne or a spaceborne instrument it is built to sense the upwelling electromagnetic radiation that is emanating from the surface which reaches the top of the atmosphere after attenuation and the TB that is registered by this instrument depends on the absorption and scattering properties of atmosphere and background emissivity which is going to vary with frequency and polarization. So let me re-itrate I am mentioning that the TB that is registered by the instrument spaceborne or airborne it is going to depend on the absorption and scattering properties of the atmosphere as well as the background emissivity which is going to vary with respect to polarization whether it is horizontal or vertical and frequency. So now look at the figure. So as shown in the figure the TB that is finally getting registered by the instrument is going to compose of self-emitted radiation from the land or sea depending upon what is the background land or sea. Then we can have upward emission from the atmosphere we can have downward atmospheric emission that is re-scattered by the surface towards the antenna together with something known as atmospheric attenuation. Attenuation is nothing but extinction of signals due to atmospheric constituents which can be water vapor which can be ozone. So essentially an interpretation of microwave brightness temperature that is TB is going to reveal the physical properties of the media that produces them, isn't it? And knowing the atmosphere the surface environmental parameters and the radiometer characteristics we can use something known as a radiative transfer model. Let me write it down. Radiative transfer model abbreviated as RTM we can use an RTM to normalize the measured TB to a common reference for comparison. Once again knowing the atmosphere the surface environmental parameters and radiometer characteristics and RTM or a radiative transfer model can be used to normalize the measured TB to a common reference for comparison. Please note that again I am introducing a new term to you namely radiative transfer model. A model that can interpret TB that is microwave brightness temperatures from radiometers with different characteristics having different viewing geometries or different incidence angles and that operated different frequencies. Again please note that over the oceans we assume emissivity to remain constant you know. This in turn applies solely for oceans. So this implies that the variations in TB when the background is ocean the variations will be due to changes in the physical temperature of the ocean surface. Now I have tried my best to represent a small section of the land surface to give you an idea that it is heterogeneous. It can have vegetation, it can have urban areas. So for land the scenario is totally different and unlike oceans it is very, very complicated to model the land surface properties in the microwave region. This is because there is huge spatial and temporal variability of soil features like roughness, vegetation cover and moisture content. Now oceans they just provide a stable and uniform cold background for a radiometer. I am using the term cold background. They provide a stable and uniform background for a radiometer and emissivity of sea surface in turn it is dependent on the dielectric properties of salt water. Emissivity of sea surface being dependent on the dielectric properties of sea water represented by the Fresnel equation. I will not get into the details of that. Just to give you an idea that sea surface it presents a cold background for a radiometer. Now over land in the presence of vegetation the microwave radiation gets emitted, absorbed, scattered with the properties mostly controlled by vegetation density, dielectric properties and relative size of vegetation components with respect to wavelength. Homogeneous, heterogeneous, oceans land and for land the surface whenever there is an increase in the vegetation density say the Amazon rainforest whenever there is an increase in the vegetation density that in turn is going to increase the emissivity in horizontal polarization, horizontal polarization and it reduces the emissivity polarization difference. Now we will discuss about them briefly through this module but for now I want to introduce the concept of a forward model to you forward model. For a passive sensor or for a sensor operating in the passive microwave region I am introducing a generic forward model to you which can be top of atmosphere brightness equal to transmissivity of entire atmospheric path multiplied by some of downwelling radiation scattered by the surface and surface brightness temperature plus upwelling radiation from the atmosphere. So what is this? This is a generic forward model that I am trying to introduce for a passive sensor for a sensor operating in the passive microwave region. Now you may have noticed a term here known as transmissivity of the atmospheric path. See actually the transmissivity of the entire atmospheric path it is better described using the vertical height rather than the path length. So if we were to write an expression for the transmissivity of the entire atmospheric path it is going to be something like this. Transmissivity equal to e raised to minus tau by cos theta. Please note that the ideal conditions for viewing a surface occur when the atmospheric transmissivity is very high which is when the frequency is less than 20 gigahertz. This will give an explanation to why some of the satellites have sensors operating in these regions. Now on a related note the scattered brightness temperature from the surface which is the downward emitted radiation from the atmosphere which in turn is getting scattered towards the radiometer that can also be written as a function of emissivity. The scattered brightness temperature from the surface which is the downward emitting radiation from the atmosphere which is in turn getting scattered towards the radiometer have used an expression to get the scattered TB value which is nothing but 1 minus emissivity into TD downward emitted radiation from the atmosphere. Now what we will do is this was this lecture was actually a summary of few key terminologies to help you understand that now we are discussing about passive microwave remote sensing. You can think about it as a camera without flash wherein naturally emitted radiation from the earth's surface is measured in the microwave region. So now I want you to forget about the discussion on radars and radar equations because we are starting a completely new module passive microwave remote sensing and what we discussed today was the few key terminologies and a small introduction about forward model for a passive sensor and then we discussed about Planck's law, Rayleigh-Jeans approximation and how ocean and land surfaces offer different backgrounds for a passive sensor. So what we will do is along with understanding the fundamentals we will also learn how passive microwave remote sensing can be applied to the field of hydrology especially to measure precipitation from space and soil moisture from space. Let me hope that you understood the initial part of this lecture and I will meet you in the next class. Thank you.