 to today's lecture. So just to share a quick recap, we are in module 5 and till now we have been learning about the fundamental principles of passive microwave remote sensing and we have been trying to understand what is a forward model and a few terminologies like emissivity and how they are related to forward model. So what we will do is this is the third lecture of the fifth module and in this lecture we will try to understand how passive microwave radiometer data is helpful in measuring precipitation. So before that I hope you remember the forward model that we discussed and we were also trying to understand the generic expression for top of atmosphere brightness using transmissivity of atmospheric path, surface brightness temperature, downwelling radiation that is scattered by the surface and upwelling radiation from the atmosphere. So you do not have to learn this expression by heart. So just take a look at the diagram towards the left side of the screen where ocean is shown, atmosphere is seen and if this is the radiometer which is looking down at the surface, there can be upwelling atmospheric TB, upwelling atmospheric TB. The atmosphere themselves they can contribute to downwelling atmospheric TB which again is getting scattered by the surface, the surface here being ocean and which is redirected to the radiometer which is on border platform which is a satellite and the surface themselves they can contribute to surface emission that is TB due to surface emission. So now we know these terms and of course transmissivity of the atmospheric path if given we can use this expression that is the generic expression for a forward model to estimate the top of atmosphere brightness that is what is the value that radiometer sees when it is looking down at the surface of the earth. Now I have taken ocean because as discussed in the previous lecture, oceans to a radiometer they provide a cold background creating contrast and making measurements about precipitation easier. So we will come to that in a short while but please make sure to remember this diagram so that further discussions are easy to understand. A quick question, assume what you see here is a radiometer, I am asking you what is r, what is the footprint size? Given the height, assume a wavelength of 1 centimeter is being used and assume the value of d is 1 meter. You can assume this value as theta the angle the angle with which the radiometer is looking down at the surface of the earth. So how do we solve the simple question? We can easily write sin theta is equal to wavelength by d, isn't it? Look at the diagram sin theta equal to lambda by d which means I can easily write r as nothing but 2 times h multiplied by lambda by d, isn't it? I am using the triangle for r by 2, so r is nothing but 2h multiplied by lambda by d. So when you plug in the values you will get 17 kilometer as the answer, simple question. For us to estimate what is the footprint size if the value of h is given, lambda is given and d is given, okay? See, when it comes to passive microwave remote sensing there are its own pros and cons that is advantages and disadvantages exist for passive microwave remote sensing and what you see in your screen is just an attempt to summarize the plus points as well as the disadvantages of passive microwave remote sensing. For example, just like the calculation you have done a passive radiometer will often have larger field of views which means the instantaneous field of view can be of the order of kilometers. It is not going to be crisp and clear like what you get in optical remote sensing, okay? And of course it does have a strong advantage for the study of weather for atmospheric sounding as we discussed in the last lecture because microwaves have the inherent ability to penetrate through clouds which means if there is a cyclone happening in the Bay of Bengal, microwave remote sensing can help us see through the cyclone core, okay? The eye of the cyclone, the vertical profile can be seen using microwaves, alright? In the advantages you see that it usually it is a highly stable instrument calibration is being followed and of course a passive microwave remote sensing can give you complete global coverage with wide swath. Radiance is linearly related to temperature and on the disadvantages of course when we look at polar orbiting satellites discontinuous temporal coverage can also be observed at low latitudes and we already know that when microwave brightness temperatures are being used for measuring precipitation over land because the emissivity of land is going to be highly variable in nature. It is going to vary due to the spatiotemporal variations in soil, vegetation, roughness because of which land offers a hot background for the radiometer which means due to the differing emissivity over land estimating precipitation using passive microwave remote sensing is challenging. I will not say it is difficult but it is challenging. We will see that shortly. So with these points in mind let us now learn about what are the applications of passive microwave remote sensing in hydrology and among the n number of applications we will try to focus on the ones that are relevant for hydrology and let us start with precipitation. When we talk about visible and infrared images precipitation is estimated by observing the cloud top temperature. You remember the diagram I showed you from INSAT 3D satellites which was very similar to the diagram you see when news is being read out especially in the weather section. So when we talk about visible and infrared images because they cannot penetrate through clouds what happens is that precipitation is estimated by observing the cloud top temperature and then they are correlated with ground-based rainfall measurements. But in the case of microwave measurements they are able to penetrate clouds and especially the frequencies below 100 gigahertz let me write that down below 100 gigahertz it is best suited for measuring precipitation because they coincide with the atmospheric windows. Remember atmospheric windows not a new term for you. So the frequencies which are less than 100 gigahertz they coincide with the atmospheric windows and hence they are suitable for the study of precipitation and at higher frequencies say greater than 50 gigahertz microwaves which propagate through the atmosphere they are affected by scattering, scattering due to ice particles and at lower frequencies there is thermal emission from liquid water droplets which tend to dominate the atmospheric effects. Now whether the microwaves that are propagating through the atmosphere whether it undergoes scattering or it does not. So all these are going to depend upon the properties of cloud you know their shape their size and so on. So in a nutshell over ocean the microwave emissivity of rain is nearly 0.9 the emissivity of ocean is much lower say nearly 0.5 and oceans they offer a cold background which enables any change in emissivity to be quickly measured through the brightness temperature and therefore it is easier to estimate precipitation over oceans by a radiometer. Let me reiterate oceans cold background and the emissivity of rain is higher so the cold background of oceans are offering some kind of contrast for a radiometer to easily estimate precipitation and in the case of land surface because there is you know because the land surface offers a hot background it is highly challenging to try and you know see for a contrast because it does not exist. So over land surface what happens is that scattering of microwaves by frozen hydrometeors is used to measure rainfall. So hydrometeors the term as such it means precipitation sized particles. So over land surface to estimate rainfall there are many physical models or empirical models to relate the scattering signature to the surface rainfall rates. Now please remember that the TB that is the brightness temperature that gets registered by a downward viewing space bond radiometer it is going to have an indirect relationship with the rainfall rate. The relationship is not going to be direct it is going to be indirect and therefore the underlying physics for rainfall retrieval they are completely different when the surface is land and when the surface is oceans. So there are you know land algorithms as well as ocean algorithms to quantitatively estimate precipitation by a radiometer using TB over land and over ocean. So two classes two broad classifications of algorithms exist and let me reiterate because you know the highly non-homogeneous land surface background it tends to have varying emissivity values. So what happens is that these varying emissivity values they add clutter to the emission from rainfall. thereby making it extremely difficult to detect the signals rainfall signals. And therefore the land rainfall algorithms using passive microwaves they have been traditionally dependent on empirical relationships utilizing the ice scattering property at 85 gigahertz channel let me write that down 85 gigahertz channel. Quantitative estimates of passive microwave rainfall retrieval indicate that although the retrieval over ocean surfaces are performed with acceptable accuracy over land retrieval based on ice scattering at 85 gigahertz continues to remain ambiguous. So this is an active area of research sharing just for information. And if we move forward we can see that there are emission based methods as well as scattering based methods. And assume a satellite bond radiometer is operating at frequency say below 50 gigahertz below 50 gigahertz. And it is capturing information while flying over an ocean say the Pacific Ocean. Remember ocean offers a cold background to a radiometer. So what happens is that the emission from the precipitation sized particles that is hydrometers can be easily detected because the cold background offered by oceans they create a contrast. Again over land it may not work because land does not offer a cold background. In some time we will discuss about the specific frequencies used by satellites to measure rainfall. But for now I want you to understand that there are two methods to estimate precipitation when it comes to passive microwave brightness temperatures. They are the emission based method and the scattering based method. So when I talk about scattering based method assume the same satellite bond radiometer which is operating at frequencies now above 50 gigahertz. So what happens is when the microwave frequencies are above 50 gigahertz now no longer is emission dominating. Now scattering tends to dominate. So I am trying to explain to you at what frequencies does emission dominate and at what frequencies does scattering dominate. So microwave frequencies above 50 gigahertz now no longer is emission dominating but now the scattering tends to dominate. So in the screen in front of you have tried to depict graphically what is meant by emission and scattering. Now the upwelling radiation that is emanating from the surface of the earth it will get scattered away from the field of view of the radiometer. And there are measures wherein we can use more than one channels more than one frequency to generate something known as a scattering index to detect the presence of precipitation. We shall discuss about these once we look at the case studies. But for now let me try to summarize the different satellite missions that contain or that operate using a radiometer. We can have the special sensor microwave imager which is on the defense meteorological satellite program. Then we have the advanced microwave sounding unit, the scanning multi-channel microwave radiometers, tropical rainfall measuring mission, advanced microwave scanning radiometer earth observing system, global precipitation measurement mission. So what are they? We can get microwave brightness temperature from the data products of SSMI, AMSU, SMMR, TRMM, GPM and AMSRE. And each of these use different frequencies for example the SMMR that is the scanning multi-channel microwave radiometer they use frequencies of 6.6, 10.7, 18, 21 and 37. Whereas the SSMI they use these frequencies that is 19.3, 22.3 and so on. Whereas AMSRE they use a different set of frequencies, different set of microwave frequencies and each of these can give us microwave brightness temperature using which we can estimate the rainfall rate. Now you may remember that in one of the earlier modules we discussed about TRMM sensors. The different sensors which are onboard TRMM satellite which is precipitation radar then there is also a TRMM microwave imager. So in the last module we spent a lot of time discussing about what is precipitation radar but now I want to highlight that TRMM also has a microwave imager wherein information is obtained in these frequency channels in horizontal and vertical polarization. H stands for horizontal and V stands for vertical polarization. You can see that passive microwave frequencies they often result in high instantaneous field of view. For example, 10.65 vertical channel it has IFOV of 59 kilometers you know 59 kilometers. So I am speaking about the major and minor axis of the ellipse which is the instantaneous field of view when seen through each of these channels. Now IFOV here stands for effective field of view. Similarly, you know as I mentioned earlier that the same satellite is carrying both a radar as well as a radiometer. Radar termed as precipitation radar abbreviated as PR and microwave imager abbreviated as TMI which stands for TRMM microwave imager. And both TMI and PR they are going to collect information in different channels. And what you see in front of you is a single orbit. Red shows the swath of TMI taken during one particular day and what you see black is the swath of PR orbit. So typically if you want to do a comparative assessment of the rainfall that is estimated from TMI that is microwave imager and the rainfall that is estimated using PR that is precipitation radar. The first step that is performed is something known as data colocation that is locating one within the other. Data colocation just to highlight that the swath of microwave imager and precipitation radar are different in TRMM data products. When we talk about GPM that is global precipitation measurement mission, GPM also has a microwave imager which is operating in different channels. Here also H stands for horizontal and V stands for vertical polarization. And as we discussed earlier the choice of which channel has to be selected for study of precipitation it is not random. You know if 23 vertical channel is chosen it is chosen for a particular reason. Remember the discussion we had on resonant frequency and the water vapor absorption lines. So the GPM microwave imager operates on several channels in vertical and horizontal polarization as you can see from this slide. Typically the GMI instrument has 13 channels wherein each channel is sensitive to a particular frequency of microwave. So the channels are so chosen that few channels are sensitive to heavy rainfall, few channels are sensitive to moderate rainfall. Again there are few channels which are sensitive to both snow and ice within clouds as well as there is sensitivity to water vapor and snowfall. So when multiple channels are involved in GMI it ensures that different ranges of possible precipitation types are being measured. So now I am curious to see how data from GMI would look like. So what you see in front of you is TB that is microwave brightness temperature in Kelvin from GPM GMI. It was taken when it was passing through the hood hood cyclone which occurred on 9th October 2014 at 06 UTC. You can see that the colors represent the temperature in Kelvin. So the range is from 200 to 300 Kelvin and towards the left side you see the figure captured in 37 V that is 37 Gigahertz in the vertical polarization and towards the right side you see the data that has been captured in 89 Gigahertz frequency for the vertical polarization. So this is how the data is going to look like and you can clearly see the parts of the cyclone, is it not. So as discussed earlier microwave frequencies they possess penetration capabilities which is why we use them to study more about cloud properties. And since the last two decades a great progress has been made in microwave based retrieval of precipitation. But remember that with the widespread acceptance of microwave based precipitation products it has also been known to contain uncertainties that is how do we trust the rainfall we get from microwave based sensors. And there are many studies which are conducted to estimate the uncertainty of microwave based precipitation products. For example, you may have the reference rainfall say they are from Indian meteorological department, rain gauges. You may have the rainfall from a microwave radiometer and we can easily compare to estimate the accuracy of microwave based precipitation products. So let us have a quick look into the same. I hope you remember the contingency matrix and measures like the probability of detection, the falls alarm ratio etc which can be derived from the contingency matrix. So shown here is the comparison of three satellite based precipitation products with respect to the reference precipitation data. So the 2A12, this is a name given to the TMI that is TRMM microwave imager 2A12 algorithm. It is also known as the Goddard profiling algorithm which estimates hydrometeor profiles by matching the observed TB with those from a pre-existing database of simulated hydrometeor profiles. So typically a Bayesian inversion scheme goes into creation of this product. I will not get into the details but just for you to understand this product comes from microwave imager. And when we talk about the 2A25, it is the name given to the algorithm 2A25 algorithm which is obtained from precipitation radar. And when we talk about 2B31, it is a combined algorithm which merges the information from both TMI as well as PR. So let me write combined here. Combined. So the guiding principle in the design of 2B31 combined algorithm has always been to merge the information content from both TMI as well as from PR. So what you see here is a comparative assessment of the rainfall over Mahanadi river basin of India. The colors note the values. Say you can see the values of probability of detection here from all the three sources, false alarm ratio from all the three sources, critical success index and miss. I hope you remember the derivations, the expressions to calculate POD, FAR, MIS etc which we have already covered. So just to show you that this is one type of analysis wherein we compare the precipitation that we get from passive microwave sensors. And we try to relate it to the reference precipitation just to do a comparative assessment of the accuracy of precipitation. Now again this is to share that there can be studies that try to use the orbital data for analysis and studies are also conducted to evaluate the gridded precipitation products. Just to let you know that a combination of TB values from different channels can also be used to check their relationship with near surface rainfall rate. So we have discussed about TRMM. Similarly, we can have comparative studies for GPM microwave imager with respect to the reference precipitation as well. In addition to the satellites that were mentioned, we also have the time resolved observation of precipitation structure and storm intensity with a constellation of small sacks abbreviated as tropics which is proposed to be launched in the year 2022. So for more details about tropics, I would urge you to visit this particular website as highlighted. So, this constellation of small satellites are aimed to provide measurements over the tropical region and each cubesat in tropics, it shall consist of a high performance radiometer which shall provide temperature profiles using seven frequencies near the oxygen absorption line, three channels near the water vapor absorption line, imaginary in a single channel near 90 GHz for precipitation measurements and a single channel at 206 GHz for cloud ice. And just to let you know that it is going to be launched in the year 2022. So what we will do is by now, I am going to assume that you as an audience for this course have been diligently following the tutorials, the exercises that were shared using Python. And so what we will do is, let me show you how to open and view a sample file for tropics which was downloaded. So as before, I have opened the Jupyter notebook and I am going to import certain libraries. The tropics data was made available as a netcdf file .nc as extension. So I am going to import the netcdf4 for plotting. I am going to import matplotlib.fiplot as plt and I am also going to import glob and numpy. Now I need to list the path. For that I am going to use glob.glob. This is for listing all the files which are having an extension of .nc netcdf. I need to view the latitude, longitude and the microwave brightness temperature pertaining to a particular file from tropics. So let me use nc.dataset command and remember each of these files are going to have a lengthy nomenclature. The file name is too long. These are the files which were downloaded as the sample. So what I will do is I do not want to make any mistake when I am typing the file name. So let me copy the lengthy file name, use it in Jupyter notebook so that there is no syntax error .nc. So now nc.dataset reads the file and then it is stored in DAT. So if you see the file name is present, the dimensions are present and most important the variables contained in the file are listed here. So now what I will do is I want to see how to extract the variable pertaining to the microwave brightness temperature. So let me follow a simple set of commands for the same and also I want to be aware of the latitude and longitude pertaining to each measurement of TB. So I am going to use for I in range 1, 329 using nc.dataset. I want to extract the values for brightness temperature as well as latitude and longitude. So let me extract the variables one by one. You may be wondering why I am using temp bright e underscore k because that is the name with which TB is saved in the file. So I am going to use the same name and I am going to extract the value corresponding to temp bright e underscore k which is going to be stored in TB. Similarly, there is a particular name with which the latitude and longitude are saved in the file. I am going to use those names to extract the value of latitude and the value of longitude. Please make sure that you do not make any syntax errors due to spelling mistakes long. Yes, let me also try to extract the brightness temperature values. So you may have you may be wondering why I am using 329 because 329 files were present in the folder which was downloaded as a sample data. I can get to display the value of latitude which is present as a mass variable. You can see the value of latitudes here. Similarly, I can display the value of longitudes. The value of longitudes and finally, I can also see the values for microwave brightness temperature in Kelvin. There you go. So what did we do? We have tried to take a sample file from tropics data and we have tried to extract the value of latitudes, longitudes and microwave brightness temperature. Remember there are n number of files present in this folder. I am showing you how to use simple set of commands in Python to extract the values of latitude, longitude and the variable of interest for me which is the microwave brightness temperature in Kelvin because this module is on passive microwave remote sensing. As we are talking about past existing as well as futuristic missions for study of precipitation using radiometers, I will also take the liberty to introduce you to Tempest which is a short form for temporal experiment for storms and tropical systems Cubesat constellation, Tempest. Now it is a Cubesat project of Colorado State University and the aim of Tempest is to demonstrate the ability to monitor the atmosphere with small satellites. Again to get more details about the upcoming Tempest mission, I would urge you to visit this website. So the radiometer onboard shall consist of a 6 U Cubesat and Tempest D shall provide passive millimeter wave observations using a compact radiometer. For more details about Tempest, I would urge you to visit this website where all the technical details about the mission are made available. So to summarize as part of this lecture, we were trying to have focused discussions on how passive microwave remote sensing can be used to estimate precipitation and what are the kind of studies that are being carried out to validate the precipitation measurements using reference data. And we also discussed about futuristic missions like Tempest and tropics and also we saw how to use a simple set of commands in Python to view the variables in sample data. So let me hope that you could find this lecture interesting and I will meet you in the next class. Thank you.