In this module, we will try to understand the wave nature of matter and it sounds quite maddening because it is very difficult to believe that matter can have wave nature. But then as we have seen that uncertainty principle sort of last nail in the coffin of board theory. So, such a deterministic approach of describing atomic structure is clearly not going to work and then in photoelectric effect the wave particle duality of light was already established. So, the question was does such a duality exist for matter as well. And first let us talk about the experiments that led to the realization that indeed matter can have wave like nature and those experiments are of electron diffraction. As we have said in the last module diffraction is a sure short sign of waves only when something has wave nature can it exhibit diffraction can it give you fringes. So, the experiment that was done well we are talking going to talk about two experiments the first well very similar experiments actually the first one Davidson-Germain experiment in this a beam of electrons from an electron gun and when I see electron gun one can think of a cathode ray tube with a hole at an end so that the cathode rays that are generated would go through the electrode and come out of the other end. So, the beam of electrons collimated beam of electrons was made incident on a nickel crystal and then the dispersed electrons were detected by a detector that could be rotated through an angle theta. And it was found that a diffraction pattern was obtained according to this n lambda or what is written here is m lambda equal to 2 d sin theta this is what tells us that even electrons can actually give diffraction and therefore have wave like nature. The other experiment quite similar was performed by G.P. Thomson. In G.P. Thomson experiment electrons from an electron source were accelerated towards a positive electrode in which a hole was drilled as I said a little while ago the resulting narrow beam of electron was directed through a thin film of nickel. So, the difference between this experiment and that the earlier experiment Davisen-Germain experiment is that in Davisen-Germain experiment it was done in a reflective mode. Here G.P. Thomson's experiment is performed in a transmission mode. Since it is done in a transmission mode one takes not a crystal of nickel but a thin film of nickel. So, what happened then is that for the electron beams that went through a screen was placed after the nickel film and a clear diffraction pattern was obtained. So, these two experiments indicate that matter manifested in electrons can have wave like nature. What does it mean? We do not know yet but then at that point of time De Broglie came in and what De Broglie did is that he said that well nature likes symmetry and nature manifests itself in two forms energy and matter. Since energy has dual nature there is no surprise that matter also has dual nature well that is only the philosophy of it rest of it is non-trivial mathematics and after doing that De Broglie arrived at this expression which one can arrive at very easily for photons for example where lambda is given by h by p where p is the momentum. So, for anything De Broglie proposed that wave nature is of course associated with a wavelength that wavelength of anything that anything can be electron cricket ball, Jupiter or dinosaur for anything this lambda is equal to h by p which is h by m v. In our tutorials we are actually going to work out the De Broglie wavelengths of things that are very light like electron and things that are seemingly like say a dust particle and maybe that is something that is a little heavier like a cricket ball and when we do that we will see for ourselves what happens to these De Broglie wavelengths and that will give us an answer to why is it that we do not see wave nature manifested in U, Me, Chair, Table all these things De Broglie wavelength is lambda equal to h by m v. So, for an electron which moves at 10 to the power 6 meters per second 10 to the power 6 meter per second is a very high speed but if we consider the speed of light there is 3 into 10 to the power 8 meters per second. So, the speed of this electron here is about 100 times almost 100 times less than the speed of light. So, it is very high but achievable. So, for an electron moving at 10 to the power 6 meters per second lambda one can calculate to be is 7 into 10 to the power minus 10 meter angstrom and that is why one can see this diffraction patterns using an atomic lattice because for diffraction to occur D separation between the planes of a lattice have to be comparable with the wavelength. If we take a lattice where the spacing is very small then we do not see diffraction. If we take a lattice where the separation is too much compared to the wavelength light just passes through. So, this value of lambda is very appropriate to be seen using an atomic lattice. So, now think of a human being weighing 50 kg moving at 10 meters per second one can work out what the wavelength will be and if you work out you will see that the wavelength is such that one cannot have any grating physically that can give you diffraction of that human being and show diffraction patterns. We will understand it better when we work out the assignment problems. But well remember what we said we had quoted Max Planck experimental results are the only truth without showing experimental results I cannot claim anything. So, here we show the experimental results of helium atom scattering and here the diffraction pattern is such for helium atoms moving at 2347 meters per second and impinging on a silicon nitride transmission grating which has 1000 lines per millimeter. So, all parameters are very well defined the calculated de Broglie wavelength is 42.5 into 10 to the power minus 12 meters. So, even for helium it is 42.5 into 10 to the power minus 12 meters rather small. So, for de Broglie wavelength for particles that are bigger you require something that is even smaller. However, for electrons in these experiments that we talked about a little while ago in both the experiments the wavelength that was calculated turned out to be in very very close agreement with that which we expect from de Broglie equation. And this is the vindication of de Broglie theory the experimentally observed result matches very nicely with what de Broglie theory predicts with all this background Schrodinger tried to develop a treatment for atomic structure. So, what did Schrodinger have in his hand? First of all particles can be waves waves can be particles and there is duality and when we say it like that nobody understands anything anyway. So, what he realized that you need a new theory if you want to explain the behavior of electrons atoms molecules and so on so forth. Also since we are handling things that are waves as well as particles deterministic theory is not going to work deterministic theory too much of determinism was the reason for downfall of Bohr theory remember. So, what we need really is a probabilistic theory and that is what is going to eventually lead to our understanding of what is the meaning of this wave nature of matter. This of course is expected to be non-Newtonian in nature but then what Schrodinger really wanted to do is he wanted to write a wave like equation for describing subatomic or atomic systems. Now the tools are all there because you know that total energy of a system like that would be a sum of kinetic energy and potential energy and then we know that E equal to h we know de Broglie relation. So, with this what Schrodinger did was the classical wave equation that existed at the time and is used even now for any kinds of waves sound waves for example any kind of wave when someone plays the tabula the wave that is generated on the diaphragm even for that wave one can use the classical wave equation. Del 2 psi del x2 is equal to 1 by c square del 2 psi del t2 well what are we what did we just say this is what we said this psi that we have written here something that keeps on coming back in quantum mechanics is the amplitude displacement from the mean position not the maximum amplitude amplitude. So, this displacement from mean position for any wave as we know from our knowledge of basic physics is a function of not only space but also time. So, what we are saying is that and this is something that is established in classical mechanics second derivative of this space and time dependent amplitude which is also called wave function with respect to space is equal to 1 by c square multiplied by second derivative partial derivative of course of the amplitude or wave function which is space and time dependent with respect to time. And in fact we are going to work this out in any case psi of x t is equal to c into e to the power i alpha where alpha equal to 2 pi multiplied by x by lambda minus nu t this is the phase this was known and de Broglie relationship was known to Schrodinger. So, what he did is he proposed an equation which is essentially a classical wave equation for de Broglie waves. Let us not forget that Schrodinger's equation is really a postulate it cannot be derived. Sometimes in some books derivation of Schrodinger equation is given that is not the right terminology you can arrive at Schrodinger equation cannot derive it in the same way that you cannot derive any of Newton's postulates their postulates they are the starting points and they hold because they are the universal truth. So, Schrodinger equation which is the classical wave equation for the de Broglie waves looks like this i h cross multiplied by del del t of space and time dependent wave function is equal to h hat we will come back to what h hat is h hat operating on psi which of course is a function of space and time what is h hat it is important to understand that h hat is the Hamiltonian operator and it is given by minus h cross square by 2 m del square by del square is del 2 del x 2 plus del 2 del y 2 plus del 2 del z 2 plus v of x where v is the potential energy. Now here for the first time in this course we are introduced to the concept of operators. What is an operator? An operator is something that well it sounds a little silly if I put it that way but it still is the best way of putting it. An operator is something that operates on a function and transforms it in some way. So, the operators that we are going to encounter most of the time are del del x del 2 del x 2 so on and so forth. So and it is important to also understand that this concept of operators is not something that came with quantum mechanics. The concept of operators was already there in classical mechanics. In fact the Hamiltonian operator was there in classical mechanics and this is the strength of Schrodinger's treatment. The entire problem we have had so far is that it seems that this when you go down to atomic subatomic scales when you talk about quantum mechanics everything is very enigmatic and what we have in those length scales is nothing like what we see around us so there seems to be a disconnect. So, the strength of Schrodinger's approach is that Schrodinger took very well established classical mechanical tool and combined it with De Broglie's expression. So, the logic of classical mechanics actually is taken forward as far as possible. If you remember in Bohr theory the quantum numbers fell from the sky. They were invoked just like that whenever there was a requirement. In Schrodinger's equation there is no quantum number. Quantum numbers will arise later on and we will see why they come. But in Schrodinger equation per say there is none. It is just a classical wave equation written for matter waves that is all that it is. So, this here is your Schrodinger equation in 3 dimensions. Del square is Laplacian del 2 del x 2 plus del 2 del y 2 plus del 2 del z 2. Now in the next step to simplify the situation a little bit we can write this space dependent and time dependent space as well as time dependent wave function psi which is a function of x, y, z special coordinates and t the time coordinate this we can write as a product of 2 functions small psi henceforth we will just call this psi small psi which is a function of special coordinates x, y and z and the other function is phi which is a function of t and the use of the small psi and small phi is quite popular. So, very often we do not even write these coordinates in brackets we just write capital psi equal to small psi multiplied by phi. The thing to remember here is that capital psi is dependent on special coordinates as well as time small psi depends only on special coordinates phi depends only on time. Why can we write like this because x, y, z, t x, y, z is special coordinate t is temporal coordinate and we can consider them separately space has got nothing to do with time if you work in the non-relativistic domain that is what we are doing now there is something called relativistic quantum mechanics but in this course we are not going to get into it here we work in the domain where time and space are completely separable. So, since they are completely separable we can write the wave functions as product of a space dependent part and a time dependent part. So, now we go back to the equation h operates on capital psi to give you ih cross multiplied by del del t of capital psi. So, we can write like this Hamiltonian operator H H hat operates on the product of small psi and phi to give you ih cross multiplied by del del t of the product of psi and phi. Now, the thing to understand is the Hamiltonian operator H what is it remember it is some constant multiplied by del 2 del x 2 plus del 2 del y 2 plus del 2 del z 2 plus potential energy time independent potential energy. So, the entire operator has no term in time it is expressed completely in special coordinates. So, we can say safely that the Hamiltonian H operates only on psi and del del t operates only on phi. And this thing is going to hold for stationary states we come back to the stationary states defined by your by by Reynolds Bohr H operates only on psi and del del t operates only on phi. So, we can write like this we can take on the left hand side we can take phi out and write phi H psi on the right hand side we can take psi out and write psi multiplied by ih cross del phi del t and then we can divide both sides by the product psi phi this is what we get H psi divided by psi on the left hand side on the right hand side we have 1 by phi multiplied by ih cross multiplied by del phi del t. Now, see the left hand side is a function of coordinates of space sorry I have missed of space here L H is a is a function of spatial coordinates I should have said and RHS right hand side is a function of time. So, they can be dimensionally consistent only if they are equal to a constant we will write that constant as W. So, we write it as W and then we can get 2 equations one is this H psi equal to W psi the other is ih cross del phi del t is equal to W phi. So, what we have been able to do so far is that we have been able to break down the time and space and time dependent Schrodinger equation into 2 equations one of which is completely space dependent the other is completely time dependent and that is what makes our life a little simple not only because the math becomes simpler but also because this space independent sorry time independent space dependent Schrodinger equation is the one that we are only going to use for the rest of the course because we are all working with stationary states stationary states are such that psi psi star is independent of time such that E is independent of time. So, there is no need for us to worry about the time dependent part of the wave function anymore in this course what we should worry about is what is this W? Well we have obtained what is called separation of variables. Well just for the records if you just solve the time dependent part of the wave equation that is very simple and that turns out to be e to the power minus i Wt by H cross. And to answer what is W we take the lesson from classical mechanics as we said in classical mechanics Hamiltonian represents total energy it is the total energy operator. So, when Hamiltonian operates on the function and gives you W multiplied by psi from classical mechanics itself we know that this W has to be equal to E energy. So, H psi equal to E psi this is the form of Schrodinger equation that is most popular among chemists because this is what we are going to use for the rest of the time. So, we can expand it a little bit and write minus H cross square by 2m del to del x2 plus vx operating on psi x equal to E psi x. So, this is Schrodinger equation. And now we have reached an interesting juncture in our discussion because it turns out that Schrodinger equation is a special kind of equation it is called an eigenvalue equation. What is the meaning of eigenvalue equation eigen in German means one you can think unique. So, eigenvalue equation is one is such that an operator operates on a function to give us back the same function multiplied by a constant. In this situation if this is the situation then this function is called an eigenfunction of the operator in question and this multiplier that we get that is called the eigenvalue. So, what we see here is that the total energy operator Hamiltonian operates on the space dependent wave function psi of x to give us an eigenvalue equation H psi equal to E psi. So, first of all the space dependent time independent wave function is an eigenfunction of the Hamiltonian operator. Secondly, the energy of the system is obtained as an eigenvalue psi of x is the eigenfunction of the energy operator and E is the eigenvalue that you get in the eigenvalue equation that we get we obtain when the total energy operator Hamiltonian operates on psi of x. So, in Schrodinger from this understanding of Schrodinger equation we see that this eigenvalue equation and eigenvalues eigenfunctions they can have rather important implications in quantum mechanics. So, Schrodinger equation is an eigenvalue equation. From here quantum mechanics really opens up because what one can do knowing this is that one can now propose the laws of quantum mechanics or as they are commonly called postulates of quantum mechanics. So, let us not forget once again that postulates cannot be derived postulates are beginning points. How do we propose this postulates by looking around and seeing what how nature manifests itself. What we have obtained so far is Schrodinger equation which is an eigenvalue equation total energy operator operates on the wave function to give us an eigenvalue equation in which energy turns out to be an eigenvalue. From this equation it is extended further and this postulates are proposed the first one is that for every classical variable say position momentum kinetic energy potential energy. There is a corresponding operator one can use in quantum mechanics. For example, for position the quantum mechanics quantum mechanical operator will be just x that is multiplied. For momentum it turns out to be minus i h cross d dx kinetic energy if you look at the Hamiltonian operator we know already what kinetic energy operator is it is minus h cross square by 2m d to dx 2 in one dimension. In 3 dimensions it is minus h cross square by 2m del 2 del x 2 plus del 2 del y 2 plus del 2 del z 2 potential energy operator actually is the potential energy depending on what kind of system it is the expression is going to change. So, first law of quantum mechanics first postulate of quantum mechanics is that there is always an operator for every classical variable every classical property of the system that you might want to know how do we know. We know the value by making the corresponding operator of that physical property operate on the wave function we will get an eigenvalue equation like we did for Schrodinger equation and the eigenvalue is going to be the value of that property. So, operators and eigenvalue equations have a very central role to play in quantum mechanics. So, if you look at this expression we can think like this that the wave function contains all the information of the system if you ask it is going to give you the information. How do you ask a question to a wave function by making the appropriate operator operate on the wave function and how does it give you the answer in the form of eigenvalue that we get. So, we can only know the value we can only have a specific value of the property if one can write an eigenvalue equation with the corresponding operator for the wave function that is characteristic of the system. So, in the next module we will start from here we will have a further discussion of what kind of operators what are the properties of operators that are acceptable in quantum mechanics and what are the other postulates of quantum mechanics and after that we will try to make sense of this entire wave business of matter because until now we have been we have an equation that describes the wave. We have sort of obtained postulates that can work in quantum mechanics. What we do not have so far is what is the meaning what is the real meaning of this wave what is the real meaning of this wave function that is what we are going to get at in the next maybe couple of modules.


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Hey everybody, welcome to another MVP Buzz Chat interview and I'm talking today with DeWayne. Hey, how's it going? Hey, thanks for having me on. I really appreciate it. So congratulations, another grand spanking new, especially at M365 apps and services MVP. So congratulations. So for folks that don't know you, who are you, where are you, and what do you do? My name is DeWayne Hyatt. I am a systems administrator for the University of Florida, specifically in the Institute of Food and Agricultural Sciences, which is a mouthful. So for short, we call it IFAS. And that's the land. Microsoft loves acronyms. So that's good. So does higher education. But that's the land grant component of the University of Florida. So I specifically support our research, teaching and extension mission at a central IT level. Very cool. So in this space, do you have like a certain focus within the M365 space? Are you a SharePoint guy? Or are you a change guy? I mean, it's yeah. And in government and in education, the expectation is you have wear a lot of hats. So my primary responsibility is actually in endpoint configuration manager. So that's what I do in server management and things like that. So we're distributed throughout the entire state of Florida. We have about 85 remote sites across the entire state. And the M365 stuff came into focus a few years ago when we were looking at server refreshes and trying to think forward about what's a good solution for the infrastructure here. And a big project that we had that I led was eliminating file servers and moving data into OneDrive and Teams, which really coincided with the worldwide pandemic. And so we were already in the process of doing those migrations, which really untethered our employees from those old busted file servers, so to speak. That's a pretty common story. It's interesting to go as I've interviewed other companies to hear how many, I mean, we knew that companies were, they had moved to the cloud was already accelerating before the pandemic. And so there's some companies that said, we really feel lucky that we had kind of concluded the majority of those moves. And so the transition into a pandemic world was really light for as far as information workers. But obviously, other companies that still maintain on-prem and have hybrid environments, there's still pains around that. But well, that's interesting. Well, so I'm always interested. So somebody who's in your kind of role in education, what was your path to becoming an MVP? It was pretty kind of unique, I guess maybe. I don't see a lot of MVPs in education. And I would love to see more because I know there are a lot of people out there doing a lot of stuff. That's one of my points, because it's difficult to get visibility when you're heads down in that in some of the sectors. Government is the same way. It's just, it's really difficult. So how did you break out of that? We're in the trenches a lot, for sure. So shout out to Dan Ray, a friend of mine that I've known for a while. And me and a co-worker, Joe Gasper, have been working pretty hard to expand the community that we have for M365 Modern Workplace training. So we started a community about three years ago that was basically how we unveiled the modern workplace to our employees. And as word about that spread, we actually ended up onboarding lots of external guests who came into that community from other EDUs to come learn with us. And so that was kind of the start of it. And then we've really taken a specific passion for what's called cooperative extension, which is a part of that land grant program. And modern workplace tools are absolutely a slam dunk for that audience because they're very distributed. The majority of those 85 sites I was talking about, we have one in every county in Florida. So there's 67 extension offices and they're just kind of all over the place. And so Modern Workplace really brings them together and is a really good glue for that sector. And so we've spent a lot of time building communities and doing public training and speaking and things like that. So those are some of the things that Dan noticed, which I really appreciate. Yeah, the theme of Dan Ray has hit a couple of my recent interviews. So I mean, it helps out a lot of people. That's awesome. I was going to ask is like, so your outreach to these other entities, but is it all still within the EDU sector within Florida? Or do you expand without that if there's other people that are an EDU that are interested in learning more? Yeah, the focus now is in that extension space, but that covers any university in the country. Even actually, the extension program is really a beautiful thing. It was established in the mid 1800s. The land grant system was started. The point of land grant was to establish a research university in each state within the United States and come up with best practices and a better way to do things because think about the importance even then of agriculture. If you couldn't farm, you probably weren't going to eat. So it was kind of a big deal. The extension program came along later in the early 1900s. When the government realized we need to take what we've learned and literally extend it to the people who live in the state so that they can learn how to do it. So our extension agents are called non-formal educators. They are out in the public doing workshops, teaching people how to file their taxes or rehabilitate some soil on some farmland that they bought. It's really all over the place. And so that is replicated in every state in the US. And so we've really found a passion for helping those folks. But extension is also exist in other countries too. It's not unique to the United States. So yeah, anybody in that space we'd love to be friends with. That's very cool. Well, yeah, that's always I guess the question for if you're for people that are in roles or in industries where they're not able to get out and just do as much out in the external community, they're more likely to be able to do something that's within the sector, within the industry. And so you see and sometimes even just within a broader, well, an education system, link out, work with other education support teams and kind of pull stuff together. But the process to becoming an MVP, of course, I always call it, it's a black box, we'll be honest. It's an award that Microsoft gives, but a key part of that is they need to know who people are. I mean, that's the downside. So there's good people, smart people doing amazing things, helping other people and for the community. But if we don't know about it, how do MVPs and Microsoft people submit names to propose them for potential MVP? So I don't know if anybody since you've announced out in social stuff that you've become an MVP, have you had anybody else within your community that's reached out about, hey, how do I become an MVP? Or is this something I can pursue? Do you have any of those conversations? Yeah, not not to that point. Exactly. But because it's like I was saying earlier, it's I don't know. I mean, I'm not that prevalent in the EDU space. But of the people that I knew, I only knew two that were our MVPs in higher education.  You should document that. And I told some of the Microsoft FTE that run those calls, like, hey, you could be nominating people. And so yeah, trying to get the word out in those higher ed circles about if you're out there teaching and helping and improving other people's lives, that's what this is about. So you could you could get this, you know? Yeah. Well, it's one of those things where so I know that the M365 is really exploding within the education sector. It was education was in broadly looking, there's always going to be those that were early adopters within it, but it's been kind of a laggard in adoption of a lot of it is because because there's been these really prevalent education platforms, these other non Microsoft platforms that are out there. And so it took a while for Microsoft to add capability and and of course, coming up with, you know, teams for EDU and a bunch of the specific solutions within that. And I'm talking about the full range from the high ed down to K through 12. And you know, so there's just there's a ton of growth, a ton of opportunity for people in the sector. So I'm, you know, excited to see somebody else in this sector, you know, becoming an MVP. Like, so I know you're brand new. Your do you have any questions about the program? Are you aware of kind of all like the the cool aspects of being an MVP? I mean, it's nice to just add it to the title. It's a good resume stuff or things out there. But yeah, you know, that's nice. But, you know, are you kind of aware of all that is Dan filled you in? I've got I've had a little bit of coaching in and I feel like as I reach out and connect with other extension agents, it is very nice to add some legitimacy, I guess to to the effort, because otherwise it would just be the way in from Florida, you know, hey, I want to talk to you about cloud stuff. And so it is nice to be able to thread that on a greeting or like you said in a job title, or display name is really nice. It helps legitimize what we're doing in the program that we've created. So I'm super stoked about that. But yeah, I've being in the edu space, a lot of the tools that I have are very similar. And so it's nice, you know, the MVP benefit is our thing, a lot of things that I'm familiar with, but there's a lot of stuff that is definitely different, you know, that I didn't know about, you know, IDs that you tag on to the end of Microsoft docs and stuff like that is is is different. And so those are things that I haven't thought about before that I'll have to start investigating and making sure I add that to my habit. Well, one of the best things about being an MVP, I mean, there's there's perks, there's get like little swag things once in a while. There's I think the absolute best part of being an MVP is the annual summit, which will hopefully get to be back in person next year again, not virtual. I mean, it's great to have the content and the access, but it's less useful. The best part is the networking that happens when we're all together in person, but is, you know, MVPs, you do have more better access to Microsoft and to the product teams, the engineering teams, and to the marketing teams, so that when you do like you'll become a, you know, a a key contact for people within your community within industry to provide feedback back to Microsoft. And while Microsoft has gotten a lot better at listening to everyone to customers and partners and, you know, they're there. I think one of the key things now is that they're, you know, most employees have a measurement that's in part of their annual commitments of community involvement, which is great to see that. But it's a lot of that is focused. A lot of the guidance that Microsoft provides is like, you know, befriend your local MVPs and provide that feedback. The big step there is that we need to provide the feedback. Microsoft doesn't benefit, doesn't improve if the complaints or the suggestions, the feedback never gets to them. And so that's something that's a key part of being an MVP. So anybody listening, if you know Dwayne, you know, yeah, if you have questions or complaints, like funnel them through Dwayne, it's a great way to do that. Well, it's very cool. So what other stuff are you doing in the community? So you're, you're, you're still running that user group? Are you doing any other speaking, any other events yet? Are you plugged into that world? One of our, one of our favorite things, my co-worker, Joe Gasper, who runs a lot of this stuff with me, we've had a podcast. We're approaching our two-year anniversary of that podcast. And it's been a lot of fun. We've been able to start getting better at having guests on and in the flow of how that works. And it's been a great learning experience, both with just how to produce one and, you know, how to buy the right microphone, you know, that kind of stuff. So that's been a lot of fun. It still has the land grant extension kind of undertone to it of, you know, that audience that we're serving. But I think that the content is probably relevant to anybody. So we've done things like recapping some of the announcements from Ignite to doing a deep dive into SharePoint or debating is Microsoft List going to kill Microsoft Planner, you know, like all that, all those things that are kind of out there that we find interesting. We'd like to talk about it on our podcast. So we've been doing that for almost two years now. Very cool. Well, yeah. Well, as a marketer, I'll tell you that probably the smartest thing you can do there to differentiate. Like it's good to serve your core audience there. But if you were to expand and do something like, you know, M365 for EDU podcast, maybe there's some of those that exist. There's plenty of room for others in that space. But if you just took that perspective, then, you know, you, you'd probably reach a, your larger audience there and market it out to all the EDU sector. But yeah, that's kind of advice for everybody. It's like, if you're, if you can be industry specific, even multi industry, like I work for a vendor for an ISV that we're a multi cloud. So we're not just Microsoft ecosystem or other ecosystems, but across multiple areas within the Microsoft ecosystem.  And it will then, it should grow organically beyond that as people find that good content that's relevant. That's my favorite thing about it really is the organic growth. The, the people who come to our community who say, I heard about this from so and so at my university. And, you know, we, we try to make sure that what we're doing is valuable to them and, you know, produce things in such a way that they can easily consume it and easily understand it. You know, we really wholeheartedly believe in the meet your users where they are mentality. And I don't want to come into a meeting with a bunch of agricultural agents and start talking about PowerShell modules and stuff for SharePoint, you know, like I need, I want to make sure that they come away from that feeling refreshed and really ultimately learning something that's going to make their digital life a little bit easier. So that's been a big part of our goal. Well, I'm telling you, you know, as exciting as PowerShell and SharePoint are, you know, that this is not for everybody, but yeah, yeah. Well, Duane, really appreciate you taking the time getting to know you. Hopefully I'll be out in your neck of the woods a couple of times this year for some of that. So looking forward to get back out there as travel start to pick up again. But for folks that want to find out more about you, what are the best ways to reach you? My LinkedIn is probably the best way to make a personal connection to me. Our podcast and newsletter is on there. So the podcast is called The Shift Show, which has a namesake from somebody you might know from the Shift Happens podcast. We love ducks. He's a great guy and we got to be on his show a couple of years ago. But The Shift Show was something that we started internally to kind of have some fun with our users and tell them like, this is really going to change things for you. So it literally is a shift in mentality. So we use that type of word play as much as we possibly can. But if you search the hashtag Shift Show on any podcast platform, you should be able to find it. Very cool. Of course, we'll have the links out on YouTube and on the blog post as well. And so Duane, hey, great to meet you. Thanks again for your time and hope to see you soon. Absolutely. Seeing people in real life again is so great, isn't it?


Good morning and welcome to the Church of the Week video with me, David Madden. Today's date is Friday the 27th of November 2020 and the time has just gone at 9.12 GMT. And this week's Church of the Week is Palladium. Now Palladium enjoyed a very bullish run in late 2019 and into 2020. I did multiple all-time highs back in the last year and at the beginning of this year. But like many other markets, it had a major decline in February on the back of the pandemic setting in. But since then, after a bit of volatility in March and April, we can see that the market has been in a fairly slow on a steady upward trend the last few weeks and months. And in fact, the highs that were achieved at the beginning of November were the highest level seen since March. So the market is making a recovery. If we take a look at the price action in the last few sessions, we can see it hasn't been powering ahead, but it's been ticking higher yet again. If we take a look at this blue line here, the 50 moving average, it was sort of dancing around it for the last two sessions, the last week or so. But it has been moving higher again. We've now hit its highest level since the 11th of November. If we continue to press on higher from here, we could be looking at targeting this zone here around 2,500. And if we go beyond that, we could then be looking back towards the highs of early March in around this zone here in around 2,549. And should we go beyond that, we could then potentially retest the all-time highs north of 2,700. Now, that's the price action, the potential price targets should the market move higher. If you take a look at what's going on in terms of the 50 moving average here, this blue line here, that comes into play just south, it comes into play at 2,334. If you go below that, we can head back down towards this yellow line here, the 100 moving average in a 2,227. Notice how the 500 moving average acted nicely as support in late October. We can also see it acting as support back in July as well. So the metric has been important in the past. It makes it more likely it'll be of importance in the future, although there are no guarantees. So just keep an eye out for those metrics in terms of the 50 moving average and also the 100 moving average. And if you go below that, the next level to keep an eye out for will be this red line here, the 200 moving average. That comes into play in a 2,149. And similar scenario, we saw that metric acted both as resistance and support back in July. So there's a couple of potentially big areas of support for moving averages should be drift lower. But just keep in mind, we have been in a nice kind of upward trend the last few months of buying on the dip has been a fairly common strategy. Now, if you are going to be trading palladium, it's a good idea to keep an eye on what's going on on the platinum market. Both those metals have a history of being in use for candidate converters, basically cutting down on emissions from engines.  This is part of the reason why the likes of both palladium and platinum have been popular in the last few weeks, the last few years. If you take a look at the kind of price action on platinum, we can see here, similar scenario, we had a major set off in March because of the overall pandemic. And then if you take a look at the price action since then, broadly speaking, it has been moving higher. If you take a look at the price action more recently, we can see that not too long ago, earlier this week, we saw platinum hit its highest level since September. So in a two-month high, not too long ago, so we can see that palladium is in broadly speaking in its upward trend. Platinum has also been broadly speaking being pushing higher. And the reason why I'm talking about this is one of the tenets of Dow theories that the averages must confirm each other. And to be fair, they're not those two metals have similarities, but they also have differences. And what that head end of Dow theory means, if markets are similar, they should be moving in the same direction. And they're likely to be moving in the same direction. And if they are likely to move in the same direction, you'd be more confident of that move. So if you think if you have a bullish view on palladium and you also see an upward move in platinum, you can be more confident that platinum is going to move higher. And conversely, if you feel that palladium is going to have a sell-off and you're also seeing a similar price action in platinum because it's a similar market, you can then be more confident of that move, but although there are no guarantees. That's all from this video. Thank you for listening. Have a good weekend.


update. Welcome folks. We have the now industrial straighten up fifty nine Nasdaq's up one twenty nine S&P's up twenty one bottom line folks fed comes out with their statement. You got Powell right now doing a news conference and it's pretty amazing. Bottom line is status called here in spades. One part that a question that Powell just answered is phenomenal man and what it is when I say phenomenal that I think they're so out of as to what is going on. They were talking about the aspect of prices wages inflation and the bottom line is that they are going out he specifically said they're going out and they think it's going to change in the second or third quarter in twenty twenty two. Okay. I believe we're in the last quarter of twenty twenty one. Okay. So you're talking about April of next year to June of next year. Bottom line they're going to let this thing run and run in a big way.  I mean forget it. There are all prices going to moon. We have inflation is raging man and they're basically saying it's not. That's all right. It is what it is. Silver silver flat twenty three dollars fifty one cents to get light sweet crude that's getting smoked. That's down three fifty eighty dollars forty two cents notes and bonds. That's not even getting smoked. Look at that. The ten years down eight takes trade one thirty twenty three thirty is our down fifteen at one sixty ten and King dollar King dollars down one hundred ninety six rate ninety three nine oh eight I think King dollars going to go for the low range once again folks that's a ninety three seven twenty nine area. The euro is up. We're one sixteen. The yen is at one fourteen the British pounds at one thirty six to one U. S. dollar. Go over the spy you get all all the indices right now trading at all time high the spy right now is trading up dollar ninety you're at four sixty three the queues that we had that that three ninety two. ABC structure up and made it man and what you're going to have out here today now we're going to get some juice in this market today you know you're already twenty three million so. They can really burn it does that's the real bottom line gold gold contract rejected lower price out here again they smoke gold on the smart and they got it down to seventeen fifty eight bottom line. It's at sea you don't want to be up and going to have out here. It's still in the rain didn't take out a swing point bottom line. Once I upright stay right there folks come right back.


So the Joint Actual Ground Station, more commonly referred to as JTAGS, is an in-theater node that provides theater missile ballistic early warning to combatant commanders to help provide battle space awareness and that vital early warning for the troops on the ground. So that is short burners or long burners, so your in-theater missiles as well as your ICBMs or Intercontinental Ballistic Missiles which are the large threats. So essentially JTAGS is providing that duck and cover notice as quickly as we can to combatant commanders which translates down to the troops on the ground. So JTAGS we receive our information, we directly receive it from infrared satellites, we process it and then we disseminate that information, we find it to be a threat whether it's a tactical ballistic missile or an event of significant importance to various areas of responsibility as a lifetime air defense member. To me it's a proud moment especially when I'm able to sit back and watch my operators actually do the job that they were trained to do that I helped train them to do and that they're able to accurately push out information.


If you don't take care of you, if you don't grow you, if you don't prioritise you, then what you're building will overtake you and what you're building will overwhelm you and you finish up serving the building rather than what you're building, serving you as it were.


Good little girl down there, man. Mama, you dead?  Oh. You realize how hard it is that you lay shot at the stand.  You walk in, I'm out, wet. I'm out, this is real wet. My face shining. Baby, you know what you did?    Your hands is wet. It's not my arm that's wet. Ugh. Ugh, my nigga. Oh, my God, man.    She ain't had that. She done did this 700 her time. I ain't no show up as nigga. I don't know what I'd do the day after that. What if you just remain a cool nigga? But then you gotta move. It's at that point you know your life changed. Like your life has changed for hell with that. At that moment, the trajectory of your life is complete. That story so hooked up, you don't even have to tell it no more. It's the nigga three seats down. Man, I don't know what's this nigga.  Exactly.  That's tough.  Damn. Damn. That's tough, man.  You're gonna be a little whole lot better.  You can't erase that.   Grantee. You don't want to be robbed. You know what I'm saying. I'll be drunk or something. I don't even know how to do it. But I feel like I know how to react to that.  Hey, you ever put a star crunch at the end of a telescope? Nigga, lose your mind. Crazy. Talk to the picture. Leave Timothy alone. That's Timothy right there. That ain't dreading, dawg. Do you know how hard well I will feel to walk up with you in the park? Talking to bitches.   Nigga, take 10 minutes to look up. Chico? Go on, man. Go on, man. My old life is over. I don't want to go back, man. That's what it is. Don't tell you. So you think you're just going to drink your problems? That's how they come to say it. Exactly. No.  She like it. Love it. You heard her screaming from the crowd. Outside. Shit.   You brought it from your job, my nigga. Put it your driveway. Your radio. Sit that lawn. You got your fatty bumming. And you hear, ah!  Dude, that wasn't a problem. Shit. Amen. They not even in the bedroom. Didn't they get out in the living room, bent over the couch? Knock on the door. Bow.  I was in my man. Whoa! What? She like. She mad? Exactly. And hit it snickery girl. Uh. Uh. A few good dogs. Listen don't let it happen to you, man. Dude. Don't let it happen to you. Dude, come on.  That's what I'm saying, my fellas. If you really love your girl, man. Hey, for real. Dude, hey. Don't do right by her if you got one, Slim.  I mean, but hey, at least try. Cause if she get out here and wanna get busy. Whoa! It's over. It's over with. You can't come back from nothing. Listen, fellas, understand this. If you don't wake up in the morning to watch it, but it don't belong to you. As long as you remember that. That's the dangerous game to play. You never had no problem. She gonna do what she wanna do with it. Your best bet is to be the best version of yourself that you can be. And hope that whatever she wants to do with it is beneficial to you. Please do not think you can control the matches cause you will get your heart broke thinking she's fool. Niggas.   They know how to maneuver. Dude, that's true. She got two whole boyfriends. She got a whole number of niggas. Think she love him more than you. Y'all playing bad, no lying together and everything. You don't even know.  Better than niggas. When you see the niggas, you gonna be like, what if I could have been left here?  Leave. Go. Got this nigga.  Exactly. The worst day ever. You come home, you got a head out. You got them caught and blew up.   Ugly. It's over with.  All in. Woo. Don't do it. Tell me, boy.  That's what I'm talking about. You got to walk out, snap. Walk out. Walk out, man.  She in that bin.  You trying to figure it out. You turn your radio down.    I'm talking about loud, nah, nah.  You get that good, that good struggle, fuck, fuck, you loving it. And you coming in the house, nigga, you been picked up from dinner. You got a whole bag of carobbers in the car, nigga.  The blue cheese. The blue cheese. We the main show that ain't with the blue cheese on the side, it's what you can do.  Y'all been laughing and playing and watching Ozark and everything. Shit was good in the hood.   Yeah, Tuesday. After a holiday too, come on, man. You just left her mom in there now. Y'all just was over there before for July or something at the cookout. Everybody ask y'all, man, so what y'all gonna do, man? Y'all gonna, y'all man. Man, y'all gonna. Y'all gonna, y'all gonna, what y'all gonna do, man?  Nigga, you think, come home, nigga, it's a nigga. Fuck. And the thing is, this nigga been fucking. The thing is, he actually wanna be with us. They different, man. They waiting on you. They not like us, man.    You got a good woman, she not just out here giving that vagina away. So if she do best believe it's some beneficial aspects attached to the nigga she giving it to.  He a better nigga. Ooh, it's gonna hurt your heart, man. That's the thing. It's gonna hurt your heart, man.  He gonna be better. Yep. Don't do everything you didn't do.  Everybody say it.    Birdie cast a note.  Most niggas get caught before they even get busted. In the text messages, nigga. Actually, this nigga ain't even matter yet. Nope. Get an MDM, Facebooks and all that. Nigga. Then she won't say nothing to you, man. They mentally different.   On her computer. On her computer. On her computer. Make you think everything cool, nigga.  Four of them better than you. Right now. Today. This weekend. Don't think it.   Woo!  The nigga got you working.  You got a job. That nigga. Y'all here, fellas. Every woman got that one nigga that they didn't want to find out they was pregnant by your wife. No, yeah. That's crazy you say that, my nigga. That's crazy, but that's crazy. We're talking about that with all camera. That's crazy you said that, though. It's always one nigga she don't want to find out that she's pregnant.   You ain't have a day unless your niggas know when they're wrong, man. That's wrong. Tell it.    It's not free, but that's what I've been telling nigga, you're not immune to it. You're not a real nigga till you've been on both sides.   Especially if you play a game.  Her life has worked just like yours worked. They believable, you ain't never been lied to smooth. I'm talking about in your eyes, eye contact, holding hands, in your face. Hick on my phone, I'm gonna take you, do whatever you gotta do. Get your pants, words, all that they smooth with. I ain't never gonna find that. Never, you'll never know, you will never know. You'll never know, until she wants you. Until she wants you to know. They can take the words right out my mouth. She can easily not, she can easily never find that. She goes to the grave, but at some point she wants you to know. And I put a timeline to get her to make it make sense to you immediately. That's how they're good, they are. The moment you see it, it's like, oh it makes sense now.     All this nigga speak French. This nigga know how to play the piano. Right. Classically.  This nigga, this is the airport doing holiday season. You can look up how much paper this nigga got.  This nigga running for city council. His mama working at the courthouse. His daddy the only black doctor where y'all stay. Exactly.  Exactly. And that's the thing, the better nigga you become, the more you'll realize how much privilege you can have in your world, man. Cause a nigga like that.  Exactly. First of all. From this nigga. First of all. All the way. So you gotta make sure you, like you said, don't invest in yourself. Yeah.  That makes you a good nigga. He spirit you, energy. You got a strong energy. You got strong energy, man. Yeah.  A lot of niggas know how no determination, no goals. Just no, no destination. Just waking up every day, hoping for the best. Yeah. Nah, it don't work like that. Watching everybody else. It don't work like that. It does not work like that. Yeah. The thing about it is, everybody right now already has some success. Yep. You believe that shit? Yep.  You already got your skills. You just got to accept that you have your set of skills. Now it's all about you grooming them and making them better, but... And really dedicating yourself to doing that. Cause it's kinda like somebody about to hire you and give you 700,000. Right. Cause the person who hired you did what you supposed to do and they curated their talent. That's why they can afford to pay you.  So that is, like you said, it's a blaring obviousness. Yep.  It looks different. It's set up is different. It doesn't matter. He knows all the lingo of the trade. Yep. He knows what that does. He has this. He looks professional. He knows what he's talking about because he switched, the whole switch to go from this man to that person. Exactly. That's a certain attention man. Right. It's possible. Whatever it is you want to do. That's the funny thing about it. Everybody got talents. We're talking about real talents. I keep saying this to everybody. I'm talking about something you can do right now. That talent don't necessarily mean being an entertainer. No.  Somebody know how to do that. Right. That's a talent. Something you can do naturally. Brilliant. That's your natural skill. Something you can do more efficiently, faster, better. Things that people ask your opinion on.  They got, it's 10 people that go into this process. Somebody had to put the windows over there. Take this wall out. You gotta have vision. Your talent might be, you might be the whole visionary. You might not be able to bring it to life, but you know how to get people to see the vision. Get everybody on one core. That's a talent. You promoted, you could get everybody in one room. Now, what goes on after that is not your fucking, that's not up to you, but you're the person that can do that. Or you know you can cook better than everybody. All the food, all the food, all the food, all the food.   That's a talent. It's a talent. It is, because everybody can't do it. Everybody can't do it.  Like that other team, that's the effort. That's the goal and that's their goal. And people get so blind about whatever they do for the money that they lose the intensity that you need to curate them type of skills in yourself. You spend it getting twisted on, spending, trying to hit the lottery. The first pitfall is you start comparing your success to other people. Exactly. You can't compare your first date to what motherfuckers got in their 10th year. Exactly. You want to see, if you want to try to compare success if you got to compare your 10 years to their 10 years. Exactly.  Before you...  A lot of motherfuckers get lost in that. It don't have nothing to do with the...  The reality is you paying attention to anything anybody else got going on is ridiculous. And it's a waste of time. Complete waste of time. Food must be eaten. Yeah, y'all forgot about that. Ain't we eating, baby? Yeah. They gonna pick up the order. How long we been going for? An hour. An hour. An hour. I'm gonna show you. Oh, right here, right here, right here. Got some old shoes on. Oh, yeah, that was good.    Oh, my God. Jesus. Wow. Wow, keep killing each other. Yeah, that's awesome.


The coldest run is my favorite thing in the world. It's the best event that we do and it's a great fundraiser for the Chamber of Commerce. So basically it's a 5k, but it's kind of like a color run, except instead of having, you know, rainbow colors we just use black, so you end up looking like a coal miner. The 2016 Finisher's Medal is symbolic of a piece of mining script. And even our bibs this year have mining script for the background. So we were kind of throwing back to some heritage and history on this one.


In today's lecture, we will look at various components of the water cycle which describes the movement of water on the ground in the atmosphere and below the ground surface. This is commonly called the water cycle or the hydrologic cycle. Then we will look at various components for example, the rainfall, evaporation, transpiration and filtration. So, these various components can be described in terms of what is the mechanism, how can they be measured and what is of interest to us as water sources engineer. So, let us first look at the water cycle or the hydrologic cycle and let us say we have these hilly areas. So, mountains here, then we have some streams, we have the ocean here, there may be some small depressions on the ground surface, there will be some trees, other vegetations, there may be some buildings. So, when the process of evaporation starts from the ocean, since this is a cycle we can start anywhere, we can start from raindrops falling on the surface, the precipitation or we can start with evaporation. So, let us start with the evaporation because this is the driving force behind the water. First it will evaporate from the ocean, it will condense as it goes up because of adiabatic cooling and form clouds. These clouds will rain, some rain will fall on the ocean, then the clouds will be moving, there will be some clouds over the land surface and there will be what is known as precipitation. So, precipitation we are familiar with the precipitation of solids in liquids during chemical reactions. This precipitation can occur in various forms for example, on the mountains it can take the form of snow, otherwise it can have rain or it may have hails. So, we will look at various forms of precipitation also. Now, once the precipitation occurs part of it will directly evaporate, solar radiation is the agency or the source of the heat energy. So, the solar radiation in the form of heat energy from the sun will cause the evaporation, the same energy will also cause some evaporation from the rainfall directly. So, this rain will not reach the ground even before that there will be some evaporation from the rain. The part which reaches the surface some of it will be intercepted by the buildings and may be other vegetation. So, this part will not reach the ground it will be intercepted before it reaches the ground and from the interception it may evaporate back to the atmosphere without reaching the ground. Some part of the interception will of course, fall down to the ground after some time. The part which reaches the ground can go in the ground known as infiltration. It may evaporate from the ground surface or it may run off over the ground and run off is one component in which we are very interested. Because this is what will govern the flow in the streams and if we are designing a project let us say irrigation project or water supply project we should know how much water is available in the streams or if we are interested in the flood control structures we should know what is the maximum flood expected. So, run off is a very important component of the hydrologic cycle and we should know how to obtain this component. Now, the part which goes into the ground as infiltration some part of it may be retained near the soil surface and is called the soil moisture. Part of this moisture will be taken up by the plants through their roots and then it will be transpired back to the atmosphere. So, we call it transpiration. There will be some water under the ground. So, let us say that there is some ground water table. Ground water table denotes the top of the water inside the ground which would be at atmospheric pressure. There will be a rock base. So, this will be rock above which this water will be standing and the water which infiltrates into the ground water some part of it may percolate very deep into the rocks and may be lost for all practical purposes and is called deep percolation. Some part of the water which infiltrates may again reappear on the surface. For example, if we have an impermeable layer let us say here then the water which is falling here infiltrating inside the ground may join the run off or may appear on the surface again. This is known as interflow and depending on how fast or how slow it appears it may be a delayed appearance on the surface or it may come very fast. The depressions on the ground surface will also store some of the precipitation. So, before the run off can start we should have some storage in the depression and that is also counted towards losses. So, once we have precipitation we will have some depression storage and once we fulfill all these depression storage requirements then there will be run off over the surface and going to the streams. Finally, the streams will run off to the ocean from ocean it will be evaporated back and this whole cycle will repeat. So, various components of the hydrologic cycle can be thought of as precipitation which can be thought of as driving all the flow although the precipitation comes from evaporation. So, we can start from anywhere in the cycle let us start from the precipitation. So, precipitation as we have seen can be in the form of snow or it can be in the form of rain. So, let us first look at various forms of precipitation. So, in the first classification we can classify the precipitation which is falling as liquid form or solid form. In the liquid form of course, we have rain, but depending on what is the rate at which it is falling we can classify this into different categories. For example, a drizzle or we can call it rain depending on what is the intensity at which they are falling. Drizzle for example, has an intensity which is very small and typically we use less than about 1 millimeter per hour. The rainfall or the precipitation is measured in terms of depth in depth units. So, when we say that there is a precipitation of 1 millimeter or 1 centimeter it indicates that over a certain area if the entire precipitation which is falling stands on that area uniformly it will have a depth of that much. For example, 1 centimeter or 1 millimeter and the intensity of precipitation is measured in terms of depth per unit time. So, typically millimeter per hour or sometimes centimeters per hour or millimeters per day centimeters per day whatever units we want to use, but millimeter per hour is the conventional unit. So, if it is precipitation is falling at a rate of less than 1 millimeter per hour we can just call it a drizzle. So, there is not really a rain it is just drizzling at a very small rate. Rain can be classified as light, medium and heavy again depending on the intensity with which it is falling. Light is typically less than 2.5 millimeter per hour same units and heavy is typically greater than 7.5 and in between we have medium. So, the liquid precipitation can be classified as drizzle, light rain, medium rain or heavy rain. In solid we can have the precipitation form of snow or ice depending on the atmospheric conditions at the place where the clouds are formed and the raindrops are formed and the place at which they are falling we can have various combinations. Snow has a density which is quite small. So, when we measure the precipitation in terms of snow we typically express it in equivalent water depth. The specific gravity of snow is typically about 0.06 to 0.15 and general value which is taken is 0.1. What it means is that if 1 centimeter of snow falls it will be equivalent to 1 millimeter of water depth. So, typically they will be measured in terms of the equivalent water depth and the measurement devices for snow would be different because the depth is very high for the same amount of precipitation. Ice again this is not very common under Indian conditions, but we can have various different kinds in ice also. For example, we can have sleet, glaze and hail. Hail has ice pellets which are typically greater than 8 millimeter size ice pellets. Sleet and glaze sleet is a freezing rain and glaze is an ice coating which is formed when the raindrops hit a frozen ground. So, ice coating on frozen ground. So, these are not very common. So, we will not study them. The liquid form which is rain is naturally what will concern us very often. So, we will look at mostly we will discuss in terms of rain. Sometimes we will talk about snow also, but we will concentrate on rain. So, let us first look at what is the mechanism. In rainfall what we require is presence of water vapor and then somehow they should condense and fall to the ground. So, if water vapor is present in the atmosphere, suppose this is the ground level and there is water vapor present in the atmosphere here. This has to cool down in order to precipitate. So, if suppose we have some air mass here which contains water vapor and it is lifted to a higher level, then this is of course cooler as we go higher in the atmosphere temperature decreases and as it goes to a cooler level they will be condensation and this will fall as precipitation. So, there should be some mechanism of creating water vapor and some mechanism of cooling that air mass to a certain temperature. So, that it can precipitate. The mechanism for cooling will decide what kind of various rainfall types we have. Typically, we can classify them as frontal precipitation, convective precipitation, porographic and cyclonic. Cyclonic also includes anti-cyclonic which have different directions of wind. In the frontal there is cold and warm air meeting. So, there is a front which has cold air on one side. Let us say this is the cold air and here we have warm air. Now, this warm air may be moving or the cold air may be moving, but the net result is that the warm air gets lifted above the cold air and as it gets lifted it becomes colder and then it will cause condensation and precipitation. So, that is the mechanism of frontal rainfall or frontal precipitation. In the convective precipitation there may be a local cooling. So, if the ground is let us say warm here, then the air which is in contact with the ground gets heated and is lifted up because the density becomes smaller and as this air is lifted up cold air from surrounding will come to replace it and therefore, it will cause a convective motion here. The cooling as this air mass goes up the cooling will result in precipitation. Typically, these occur at a small scale. For example, 10 square kilometers or so. So, the area covered by convective precipitation is generally small. Orographic in this the lifting agency are mountains. So, if the ground surface is like this, this mountain here air coming in here will get lifted because of the presence of the mountains and as it gets lifted again it will have condensation and precipitation. Typically, precipitation is more on the side which is facing the wind and on the other side precipitation will be small because this air has already the water vapor has already been taken out of this air. So, we have what is known as rain shadow that in this portion rain would be very small compared to on this side. Cyclonic and anti-cyclonic this is anti-clockwise wind movement. So, very high speed wind and anti-cyclonic has a clockwise motion and these patterns cyclones and anti-cyclones they carry a lot of moisture and they cover every large area. Typically, an area up to may be about 200 square kilometers can be covered by cyclonic precipitation. So, these are some common mechanisms which cause precipitation. So, after looking at various forms of precipitation, let us look at how to measure it and then how to analyze the data which is collected by measurement. So, let us first look at the measurement. Broadly, we can classify the measuring instruments as non-recording and recording depending on whether they get the values continuously. For example, in recording or at some particular fixed time non-recording. So, they do not record continuously with time and recording they maintain a continuous record with time about the depth of rainfall. We have already seen that measurement is typically done in terms of depth and generally in millimeters. The site for the rain gauge. So, suppose we have some area here and we want to install a rain gauge here. So, the rain gauge should be located properly and when we say proper location there are some requirements. For example, the location it should have a clear area about 5 meters by 5 meters sometimes higher than this. So, this is which should be fenced. So, that it is not disturbed the rain gauge which we install here is not disturbed by animals or other people. So, this area should be clear means there should not be any objects in that area it should be fenced. So, it is not easily accessible to others. Then the height if this is the ground level the rain gauge may be installed at some height. So, the water falls here the rain falls here or we can have a lower height. So, this height has to be decided based on various considerations. For example, if the height is very large then wind will affect the measurement. If it is very small then it is very small then their chances that there will be some splashing. So, rain drops falling here may cause some splashing into the rain gauge and whatever data we record here may not be correct. So, a small height may lead to splashes or flooding sometimes the if the rain gauge height is small then the nearby area may get flooded and it may spill over into the rain gauge causing a higher amount than the actual rainfall. So, typically the height is kept at about 30 centimeters to balance the wind effects and also to prevent the splashing. The other parameter which is which has to be decided is what should be the area of the opening and typically it is about 100 to 200 square centimeters then there is a funnel which collects the water falling on this area and deposits it in a bottle. So, we have a bottle kept here which will collect the rain water falling and with time the water level will go up. So, these are non recording gauges because a continuous record of the water level with time is typically not kept in these and what is generally done is once a day the person who is maintaining this rain gauge will go look at the water level and report that as the depth of rain during that time period. Typically in the morning around 8 or 9 or about 8.30 am the measurements are made and whatever rainfall is measured is reported as occurring in the previous day. This bottle which is kept here typically can store about 10 centimeter depth of water and if there is a severe thunderstorm and we expect that this bottle may overflow then the person has to go more frequently. So, frequent measurements during severe storms have to be made so that the bottle does not overflow. So, this is the most common non recording gauge the disadvantage is that it will not be able to capture the variation with time. So, we know that in a day there is let us say 5 centimeters of rain, but we do not know when it actually occurred or what was the intensity at different times. So, for that recording gauge is used and these generally 3 common types of these gauges are keeping bucket then there could be some weighing gauges or the 3 different types which we use they may be combined or used with a remote with some remote device to transmit the data to a far location. So, if the station is not easily accessible we can use them with some remote device which captures the rainfall recorded by either tipping bucket or weighing or a float mechanism to plot the rainfall record. So, let us look at them one by one a tipping bucket typically has a bucket which is balanced at a point water will fall in one compartment. So, there are 2 different compartments the rain will fall in one compartment at a time and when the it fills this bucket will turn and then this bucket will assume its place and then the rainfall will be captured in this bucket. So, on an average there is some capacity of the bucket which if I draw a bigger figure. So, as soon as this bucket fills it will trip and that tipping will actuate some circuit and it will record it on a graph paper. So, this time of filling will be recorded and we will know how much time it will take to fill this bucket capacity and the capacity of the bucket. So, typically it is about 0.01 while filling this much means that one tip of the represents some amount which may be 0.01. This amount is dependent on us what design we make if we have a very small capacity then there will be more frequent tippings and some amount of rainfall may be lost during tipping. So, when the time which it takes for this bucket to tip over in the other bucket to come in its place whatever rain is occurring during that time may be lost. So, that is why we cannot have very small capacity also and if we have very big capacity suppose the bucket has a large capacity then there is a possibility that it may not be filled completely and it will stop during some time. So, whatever water is there in the bucket may not be recorded because this rainfall has actually occurred during some time but if it has not filled the bucket it will not tip it and it will not be recorded and when next time there is some rain which occurs it will fill the bucket and will tip it and therefore, the rainfall will be recorded as occurring at some other time. So, tipping bucket is a recording type of rain gauge because it will record continuously what is the time it takes to fill certain capacity. The weighing type of rain gauges are quite simple in mechanism. So, there is a weight measurement device here. So, whatever rain is occurring it will increase the. So, there is some weighing device here which will continuously record the weight of the container and the water in it. So, with time it will give us a constant record. We can convert or calibrate that weight to give us the depth of rain and this will be accumulated depth. So, suppose we start at t equal to 0 with 0 depth we will get a curve which will give us temporal variation of the accumulated depth and looking at this curve we can see where the intensity is high. For example, the slope is large means the intensity of rainfall will be higher and some portions the slope may be flatter. So, here the intensity of rainfall is lower. So, weighing type gives us a continuous record of accumulated depth with time. Similarly, a float type works on similar principle that there is a float and with the water level the location of this float will always be at the top of the water level and therefore, by measuring the if water level rises here then the float will come here. So, the location of the float at different times will give us the rate of accumulation of or the time variation of accumulation of water inside the gauge and it will give us again a continuous record. When the water reaches at the top there is some mechanism which will siphon this water out and then the float will again reset back to the bottom and then will again increase with further rainfall. So, all these three types of all these three tipping bucket weighing type and float type they are recording gauges which give us continuous record which is very useful for us in analyzing at different times what is the amount or what is the intensity of rain. Once we collect the data we will have to analyze it using some techniques. So, the next thing which we look at is data analysis. So, first we will see how to present the data. The two commonly used techniques are one in which we plot the intensity of rain and in the other we plot the cumulative depth. So, in the intensity of rain generally we will be using some units like millimeter per hour and cumulative depth we can use millimeters or sometimes centimeter. This is known as a hyatograph and this is known as a mass curve. So, the hyatograph will look like this suppose we have a non recording gauge where we are measuring the rainfall every day. So, for one day so this t may be expressed in days. So, for the first day we know what is the amount of rain. So, we can assume that that is the average intensity over that day although it is not a very good assumption, but if we assume that then we can plot a hyatograph like this. Typically the rainfall will not be constant over a period of a day typically it will be a few hours over which the intensity is constant. So, a hyatograph shows us the plot of intensity versus time generally in hours. While the mass curve shows the accumulation of rain as we have seen for example, for a weighing type weighing bucket type of gauge it would show us a curve like this which tells us that there is a very intense rainfall here almost no rain here and then again some rainfall here. So, this tells us the cumulative depth and the slope of the mass curve will give us the intensity at that particular time. The location of the gauges as we have seen there are a few limitations on how to locate the gauges for example, open area near that height also has to be decided, but the network of gauges has to be also properly designed. So, not only the location, but the density also has to be clearly defined. So, the density is typically defined as number of gauges per unit area where the unit area may be taken as kilometer square or sometimes we would use since the areas typically are quite large. Let us say that we take a unit area of 1000 kilometer square how many gauges will be put in that unit area will depend on what type of area it is how the rainfall is varying in that area and there are some guidelines for example, in plain areas typically 2 rain gauges for 1000 kilometer square are suggested. If we have hilly areas then we may increase the number of rain gauges to about 4 to 8 and in between for example, if we have an area which is 1000 meter elevation then we may use 3 to 4 gauges. So, that decides how many gauges we want in a particular area. Now, in this area how do we locate the gauges for example, there may be one gauge here one here one here density once we decide the density we have to decide where to locate the gauges also and in addition to this empirical guideline there is another technique of deciding the number of rain gauges in an area which depends on what is the variation of rainfall within these gauges. So, for example, if we have an area and we have some existing gauges let us say we have these m gauges. So, for these m gauges we can find out the coefficient of variation C v which can be defined as summation of over all the stations m p i minus p bar whole square m minus 1. So, this coefficient of variation represents how much the precipitation values at each gauge are different from the average this is the standard deviation sigma divide by the average precipitation p. So, C v tells us standard deviation as compared to the mean precipitation where p bar is the mean precipitation which can be obtained as 1 to m p i. So, if we have m number of gauges in the area we can find out the mean precipitation using this formula we can find out the standard deviation using this and then we can find the ratio of those as the coefficient of variation C v typically there is some allowable error which allowable value which we call epsilon and generally it would be about 10 percent. So, the allowable error or allowable variation which we have in our data or which we can permit in our data is typically taken as about 10 percent. So, if C v is below this value then it is otherwise we will have to increase the number of stations. So, the value of n which is the number of gauges which we want for the error to be less than allowable error is given as C v over epsilon whole square. So, once we find the coefficient of variation and we know the allowable error value then we can find out the number of gauges required to achieve that error and whatever remaining m gauges are already existing. So, whatever remaining n minus m that we will have to add to get our error within the allowable limit. So, this is about the network design. So, this will tell us about in this area how many additional gauges have to be put. Once we decide that then there may be some other problems once we collect the data when decide the rain gauge density we monitor it on a daily basis or continuous recording gauge basis then we need to analyze this data. The data as we have seen can be presented as either a hydrograph or a mass curve, but analysis of data there may be various problems with the data. For example, there may be some data which is missing there may be data which is inconsistent. So, missing data means that we have a long period of record at a particular rain gauge and surrounding rain gauges also, but part of it may be missing. For example, in a year we are measuring rainfall every day, but one day or two days the data may not be there. Inconsistent data means that inconsistency it may be because either a station is shifted or surrounding conditions changed. So, station shifted means we had a location of the station earlier, but due to some reasons the station has to be shifted to some other location then the data will be inconsistent because the characteristics of the areas will be different or we may not shift the station, but the surrounding area has some change in the condition. For example, obstructions may have been created or constructed near the rain gauge or the environmental factors may be some forest was there and there is a fire which changed the nature of the surrounding area. So, all these will cause some inconsistency means the data before that change and after that change will not be consistent. And sometimes we may have observation errors also for example, we may have noticed after plotting the data we may notice that before certain time the data is not consistent it may be because of some observation error also. So, human error also we can add, but it is not very likely, but there may be some observation error. So, if we have a missing data or inconsistent data we first need to fill in the gaps. So, we need to either fill in the missing data or we need to correct the inconsistent data. So, there are methods for correcting the inconsistency or filling in the missing data. For missing data suppose we have this area in which there are stations here and all of these are measuring the rainfall. We did not discuss it earlier, but in an area typically if there are number of rain gauges it is generally thought that about 10 percent of them should be recording rain gauges. So, that we can get an idea about the temporal variation also. So, if we have some missing data and there are some recording rain gauges or non-recording rain gauges we can take help of the nearby rain gauges. Suppose this is the station at which data is missing for certain period, but for the same period data is available at all these other stations. Then the equation which we can use to estimate the missing data here is p x again going from 1 to m over m. This tells us that we can. So, this is the station x at which the data is missing. So, the precipitation at x can be taken as the mean of the precipitation at all the surrounding or nearby gauges. This normally will work well, but sometimes it may create problem when the normal precipitation at the gauges. So, at these gauges and at x the normal precipitation itself may not be identical. So, suppose this rain gauge in general receives more precipitation than this then taking an arithmetic mean like this will not be proper and then we will have to modify this as again the summation going from 1 to m. So, for all rain gauges we take the ratio of the precipitation divided by the normal value. So, this normal is typically a 30 year average. For example, suppose the data is missing for 1st of January then we say over the last 30 years what is the average precipitation on the 1st of January at various gauges and that is n i or n x for the gauge under consideration. So, we say that the ratio of precipitation on that day to the normal rainfall on that day should be the arithmetic mean of the similar ratios for the other stations. So, this will help us identifying or filling in the missing value p x. Once we have completed the record by filling in the missing values we should check on the consistency. So, for checking the consistency we use a procedure which is commonly called the double mass curve analysis and the double mass curve again if we have a gauge here and we want to check its consistency we have some surrounding gauges also generally about 10 gauges are taken or neighboring gauges. So, all these gauges are taken and what we plot is the accumulated mass accumulated as average of surrounding stations and what we will do is we will plot it versus the mass accumulated mass. So, suppose x is the station for which we want to check the consistency accumulated mass at x will be plotted against the average accumulated mass at the surrounding stations which may be about 10 n number and if the data is consistent then it should plot as a straight line. So, for example, we may have let us say we talk about annual values. So, annual precipitation so we will have here years let us say the data looks like this these will indicate different years and they are plotted in reverse chronological order. So, these are the newest values and then it will time is decreasing. So, ideally they should plot on the same line if the data is consistent because then the mass accumulated mass of precipitation at x should have a certain definite ratio with the surrounding areas. But if the data is not consistent then we may have a deviation may be like this or may be like this. So, for example, the data for 2004 may be here, 2000 may be here and may be let us say 1990 is here. So, this tells us that in 1990 something changed at the station and the data is not consistent either the station was moved or environment around the station was changed and therefore, we need to correct the earlier data and bring it in line with the recent data. So, if the data is here we have to move it here on the line. So, there is a correction factor which has to be applied to all the data before 1990 and that correction factor will depend on what is the value to the line actual value a and the observed value either here or if the observed values are here then it will be up to that line. So, a is at any time what is the value to the actual straight line o is the value on the observed data if the data is here then o will be smaller if the data is here o would be larger. So, all these values have to multiplied by a by o to bring it to the straight line. So, this way we can correct any inconsistency in the data. So, by filling in missing data and by correcting in consistent data we can be sure that now we have a record of rainfall over a particular area which represents the actual conditions without many errors. The area which we have taken till now we have not really defined this catchment area, but whenever we take this area typically it is done in such a way that the boundary corresponds to a watershed. So, the rain drops falling on this side will move towards this side and the rain drops falling on this side will move towards this side. So, when we say this is the watershed any rainfall falling in this area will move towards this side this is called the catchment area for a channel. The rain gauge location may not correspond to a catchment area the rain gauge location typically when we say that suppose this is an area in which there are some rain gauges these give us a point value at a certain location. So, when we say we have the precipitation record at this point it represents the precipitation record at a single point. Our aim would be to extrapolate or to find out an average aerial precipitation. So, the next step which we have to take is how to transform these point values to represent an average depth over the entire area. For example, if this gauge collects 1 centimeter of rain this collects 2 centimeters this collects 1.5 then over the entire area what could be assumed as an average of precipitation. So, our next aim would be to look at how to convert the point values. So, these are the point values to an average depth of precipitation over the entire area and typically when we talk about this area it should be of uniform characteristic it may not correspond to the catchment area for a river, but it should be of uniform climatological conditions. So, that we can compare the records of different rain gauges. So, in today's lecture we have looked at the hydrologic cycle in which we discussed various components of the cycle really describing the movement of water in the atmosphere on the surface of earth and below the surface of earth. Then we have discussed various components of this water cycle which are precipitation, evaporation, transpiration, interception and depression storage, infiltration, ground water then runoff as surface runoff and subsurface runoff interflow. So, all these components we have described and then we said that some of these components are of importance to us as water sources engineer. For example, evaporation from the sea is really driving all the precipitation, but precipitation is causing the runoff. So, we should since we are interested in runoff because we want to see as a water supply project or irrigation project how much water is available or as a flood control project how much flood we have to accommodate in the storage reservoirs. So, we are interested in runoff, but since precipitation is causing the runoff we should look at the precipitation and precipitation data is more easily available than the stream flow or runoff data. So, we have looked at the precipitation, what are the mechanisms, how it can be measured, what are some problems with the data which may arise and how to take care of those problems and then we would look at converting these point values to aerial values because we want precipitation over certain area what is the average depth of rainfall. So, that we can convert that into some volume and therefore, that will be our next lecture how to convert the point values to aerial values.