Now some 40-odd years after his death Ludwig von Mises is actually better known and better read Than he ever was in his lifetime, and I think that's a tremendous achievement and a big part of that I Think was due to the efforts over the years of Lou Rockwell Who's the founder and chairman of the Mises Institute and someone who's known dr. Paul for many many decades So please a round of applause for Lou Rockwell Like Jeff dice I had the rare honor of serving as Ron Paul's congressional chief of staff and I've got to observe him in many proud moments In his presidential campaigns in his congressional campaigns People sometimes today compare Ron Paul with Bernie Sanders The comparison of Bernie to Ron goes something like this Both launched in surgeon and I establishment presidential campaigns while in their 70s They shook up their respective party establishments and Attracted large youth followings But Bernie is no Ron Just on the surface. He's a grump and very difficult to work for Ron on the other hand is a kind-hearted gentleman who always showed his appreciation For the people in his office and as in his campaigns More importantly countless high school students and college students began reading difficult treatises and economics and political philosophy because Ron encouraged them to do so Ron's followers throughout the years were curious enough to dig beneath the surface of the state as a benign Institution that can costlessly provide whatever we might want But there might be moral economic and political factors standing in the way of these utopian dreams It's not hard to cultivate a raving band of people Demanding other people give them their things as Bernie Sanders does Such appeals arouse the basest aspects of our nature and will always attract a crowd It is very hard on the other hand to build up an army of young people Intellectually curious enough to read serious books and consider ideas that go beyond the conventional wisdom They learned in school about government and the market It's hard to build up a movement of people like these whose moral sense is developed enough to recognize That barking demands and enforcing them with the state's gun is the behavior of thugs not of civilized people and it's hard to persuade people of the counterintuitive idea that society runs better Individuals are much more prosperous when no one is in charge of it all Yet Ron accomplished all these things As the person who reached more people with the message of liberty than anyone else in our time And maybe in any time Ron has also brought home how that message can and must be spread I want to talk about five of these lessons The more on the subject of war cannot and should not be avoided first and foremost Ron is a critic of the warfare state Ron is not a pacifist an ancient charge against those who oppose constant war He believes in the right to self-defense But he does not believe in the initiation of violence whether by private criminals or the state The state has recently taken more than a million lives in its imperialist anti-muslim wars Ron Paul has opposed them with all his heart and soul He is a man of peace and the golden rule in its private life as well as in policy The war in Iraq Which was still a live issue when Ron first ran for the Republican nomination Had been sold to the public on the basis of lies through a transparent and insulting even by the government's standards the devastation in terms of deaths Mamings Displacements and sheer destruction Appalled every decent human being Yes, the Department of Education is an outrage But it is nothing next to the horrifying images of what happened to the men women and children of Iraq If he wasn't going to denounce such a clear moral evil Ron thought what was the point of being in public life at all Still this is the issue strategist would have him avoid Just talk about the budget talk about the greatness of America Talk about whatever everyone else is talking about and you'll be fine and they neglected to add forgotten But had Ron shot away from this issue there would have been no Ron Paul revolution It was his courageous refusal to back down from certain unspeakable truths about the American role in the world That caused Americans and especially students to sit up and take notice While still in his 30s Murray Rothbard wrote privately that he thought that war was the key to the whole libertarian business unquote This is another way Ron Paul has been faithful to the Rothbardian tradition time after time In interviews and public appearances Ron has brought the question posed back to the central issue of war and foreign policy Worried about the budget You can't run an empire on the cheap Concerned about the TSA Groping or government eavesdropping Or cameras trained on you These are the inevitable policy results of the hegemon In case after case Ron pointed to the connection between an imperial foreign policy abroad And abuses and outrageous at home Inspired by Ron Libertarians began to challenge Conservatives by reminding them that war after all is just the ultimate government program War has it all propaganda censorship spying crony contracts Money printing skyrocketing spending debt creation central planning hubris Everything we associate with the worst interventions into the economy But Ron Paul permanently changed the nature of the discussion on war and foreign policy The word non-intervention rarely appeared in foreign policy discussions before 2007 Opposition to war was associated with anti-capitalist causes That is no longer the case Ron kept insisting that there was no real foreign policy debate in america because all we were allowed to do Was decide what kind of intervention the u.s government should pursue Whether intervention itself was desirable or whether the bipartisan assumption behind u.s foreign policy was sound This was not even mentioned much less debated In exposing the fraudulent american foreign policy debate ron exposed an overlooked truth about american political life The debates americans are allowed to have are ones in which the real decisions have already been made Income tax or consumption tax fiscal stimulus or monetary stimulus Sanctions or war Later war or war right now With debates like these it hardly matters who wins Ron pulled back the curtain on all of this to tell the truth It wasn't just on war that ron defied the censors of opinion Ask ron paul a question and you get an answer In miami he said that the embargo on cuba needed to be lifted In south carolina he stuck to his guns on the drug war He never ran away from a question or twisted it in spin doctor fashion Into a question he wished that he'd been asked in typical political fashion And the audiences kept growing Thousands and thousands of students were coming out to see him at a time when his competitors barely fill half of bingo hall ron knew that the philosophy of liberty When explained persuasively and with conviction had a universal appeal Every group he spoke to heard a slightly different presentation of that message as ron showed how their particular concerns Were addressed and most effectively by a policy of freedom When ron first spoke to the so-called values voters, for example, he was booed for saying that he worshiped the prince of peace The second time when he again made a moral case for freedom. He brought the house down But he did not pander to them nor to anyone else And he never abandoned the philosophy that brought him into public life in the first place No one had the sense that there was more than one ron paul That he was trying to satisfy irreconcilable groups There was one ron paul Number three the problem is not one person or one party ron rarely gets worked up over some government functionary who had been receiving some graft Yes, this is wrong. Yes, the guy should be sacked And maybe punished more significantly But to spend inordinate time on the scandal of the day is to suggest that if only we had good people in government The system would work The vast bulk of what the state does of course shouldn't be done at all by anyone And it doesn't matter whether they're good or bad people. You can always be managed far better by free individuals If a government official spends inordinate sums on vacations And luxuries or is exposed for being on the take Be assured that the person's political opponents will be all over the story Meanwhile, the inherent corruption of the system itself with a systematic expropriation and redistribution is ignored But that is by far the most important story and it's the only one that really deserves our attention Number four there is more to life and more to liberty than politics Before leaving washington and electoral politics ron delivered an extraordinary farewell address to congress The very fact that ron could deliver a wise and learned address only goes to show He was no ron of the mill congressman and whose intellectual life is fulfilled by talking points and focus groups results That a farewell address seemed so appropriate for ron in the first place while it would have been Visible for virtually anyone of his colleagues reflected ron's substance and seriousness as a thinker and as a man In that address ron did many things He surveyed his many years in congress He made a reckoning of the advance of the state and the retreat of liberty He explained the moral ideas at the root of the libertarian message non-aggression and freedom He posed a series of questions about the u.s. Government and american society that had hardly ever been asked much less answered And he gave his supporters some advice on spreading the message in the coming years Quote achieving legislative power and political influence. He said should not be our goal Most of the change if it is to come will not come from the politicians But rather from individuals family friends intellectual leaders and our religious institutions The revolution and the solution can only come from rejecting the use of coercion compulsion government commands and aggressive force To mold social and economic behavior Number five the fed cannot be ignored No focus groups urge ron to talk about the federal reserve No politician had made an issue of the fed in its 100 years Stick to the script the professionals would have said lower taxes and lower spending The monotonous refrain uttered by every single republican politician who typically has no interest in doing either Yet ron pointed to the fed as the source of the boom bus cycle that has harmed so many americans His dogged insistence on this point got a great many americans curious What after all was the fed and what was it up to? An unlikely issue to be sure and yet it was his willingness to talk about it Is in my view helps to account for much of his fundraising success There was a small but untapped portion of the public that responded with enthusiasm to ron's very mention of the fed And they wanted more Here again had ron adopted some conventional political advice He would have forfeited these historic moments and the ron paul phenomenon would have been greatly diminished If not compromised altogether Only a few months after ron officially suspended his 2008 campaign the financial crisis struck Just as ron had said there was something indeed very wrong with the economy Because he hadn't hesitated to say what he believed even if it meant dealing with an issue No political operative would have encouraged him to discuss ron was a profit That point alone opened countless more people's eyes to ron's ideas and their minds There was just one guy in washington who warned us of what was to come And coincidentally there's been a time in american history in which more people were reading and writing Anti-fed books because of ron paul. I would argue People could see too that ron hadn't just gotten lucky in 2007 and 2008 In 2001 ron said on the house floor that the fed fueled bubble in tech stocks Which had just burst was being replaced by a fed fueled real estate bubble that would in its turn Bust just as surely Of course, it's not enough just to get rid of the fed Essential as that is we need sound money And for ron following mesis and Rothbard. This meant the gold standard Once when ron was invited on the other ron's air force one for a flight to houston Ron paul commented on reagan's watch, which was made from a $20 gold piece He said I wish we still had that monetary system You know reagan responded no nation that abandons the gold standard has remained great, unquote Reagan was told by his advisors never to bring that up again and never to say anything like that again 1982 ron paul served on the us gold commission to evaluate the possible role of gold in the monetary system In fact the commission was his idea It was carrying forth a promise made to the republican platform ron couldn't pick the members So from the beginning the deck was stacked The majority was dominated by monetarists who saw gold as too scarce and paper as just fine But ron's team was ready with his marvelous minority report Rarely has the dissent on a government commission done so much good The result was the case for gold and it was the greatest result of the commission It covers the history of gold in the united states Explain that its breakdown was caused by government and explains the merits of having sound money Prices reflect market realities Government stays in check and the people retain their freedom The scholarship and rigor impressed even the critics of the minority Ron and lewis lerman worked with a team of economists They included murray roth barry Murray was the main author so it's hardly surprising that such a book would result I'm convinced that the historians whether or not they agree with them Will continue to marvel that ron paul for many many years to come Was able to do what he was able to do Libertarians a century from now Will be in disbelief with the very notion that such a man could serve in the u.s. Congress of our time One of the most thrilling memories of the 2012 campaign Was the sight of those huge crowds who came out to see ron His competitors meanwhile couldn't fill a starbucks When I worked as ron's chief of staff in the late 70s and early 80s, I could only dream of such a day What was it that attracted all those crowds to ron paul? He didn't offer his followers a spot on the federal gravy train He didn't pass some phony bill He didn't do any of the things we associate with politicians What his supporters loved about him and love about him Was that nothing to do with politics at all Ron is the anti-politician He tells unfashionable truths Educates rather than flatters the public and stands up for principles even when the whole world is arrayed against him Of course ron paul deserves the nobel peace prize And the ron paul institute was last night awarded the first mary rothbard peace prize Very well deserved to this to this institute And of course in a just world he'd also be awarded the medal of freedom and all the honors for which a man in his position Is eligible But history is littered with forgotten politicians who were in piles of rewards handed out by other politicians What matters to ron more than all the honors and ceremonies in the world is all of you And your commitment to the immortal ideas he has championed all his life It's ron's truth-telling and has urged to educate the public that should inspire us as we carry on into the future Little did he know those thankless years of pointing to all the state's lies and refusing to be absorbed into the blob Would in fact make him a hero To see ron speaking to many thousands of cheering kids when all the respectable opinion Have been warning them to stay far away from this man is more gratifying and more encouraging than i can say Was especially thrilled when a tempestuous ron responding to the establishment's description of his campaign as quote dangerous Said you darn right. I am dangerous to them Even the mainstream media had to acknowledge the existence of a whole new category of thinkers One that is anti-war anti-fed anti-police state and pro-market The libertarian view is even on the map of those who despise it That too is ron's doing Young people are reading major treatises in economics and philosophy because ron paul recommended them Who else in public life can come close to saying that? No politician is going to trick the public into embracing liberty even if liberty were their true goal And not just a word to be used in fundraising letters For liberty to advance a critical mass of the public has to understand and support it It doesn't have to be a majority or even anywhere near it But some baseline of support has to exist That is why ron paul's work is so important And so lasting Thank you


Thank you very much for coming to the translation management strategy for editors in Drupal 10. I'm Jeremy Chinkwist. This talk was given actually a few months ago more from a developer perspective with a colleague of mine Leopold Novelli. But this one's been adapted a little bit more for us as content users or creators. First off, this in general is the page that we have. It's built with the layout builder that we would like to have a translation for. And so just a quick question, but when you look at this page, what do you think needs to be taken into account when doing translation? I just have to repeat it, but if you say it out loud, come on, the menus, okay? There's nothing yet, nothing else to the translation, nothing? The what? The content of it? Translating the text? Sorry, louder? Yeah, the links, definitely. So yeah, we'll get into some of those specifics. A lot of other elements, for example, the image, whether or not you have two different images for the translation. It's actually how also the language switcher itself works. Is it taking the browser default and then switching? Is it doing other things? So there's a lot to actually keep in your head when you're actually dealing with the translation of a website. It's not simple by any means. So we actually wanted to take our marketing website, which had several features. We were going to also make it then English and German. It's a decoupled website. And for those technical people out there, we did it building on our lupus decoupled set up. It's available. There's a link later on. So we're actually talking front end to back end. These are the links, as you can see. It's just a fully integrated solution for our headless distribution. We have an endpoint that needs to be also changed when we go to multilingual. So this I kept this up here. You not only have the whatever the portal, whatever that's doing, but you have to actually adapt this so that you're getting the language specific components as well. Anyhow, pretty much enough for all of the technical stuff. Let's actually move on to the question. How can translations be made simple using the layout builder? So that what I showed you at the beginning. Here's what the back end looks like. This is a typical layout builder page. You have your different elements. You have your sections here, which are going across the entire page. You can add sections or rows. You've got blocks that you can create. So think of like paragraphs that you can add to specific block sections. And then you have the ability to create, to delete, to update any of these blocks. And we'll come to that. So again, the front end looks like this. You'll want to actually set up the translations. You'll want to be able to do create, update, delete of those translations. You'll also have to do things like manage media entities. So the relationship to the image or video or whatever. So there's actually two approaches. And we looked at both of those approaches. There's the asymmetrical and the symmetrical. First off, I'm going to show you the approach that we didn't go with. The asymmetrical approach has a Drupal module in there. So you can actually install it right away. This approach, got out of order. Okay. Yeah. The asymmetrical approach, basically, you are generating a node or content article. And then you're also generating a completely independent article for that other translation. So everything happens detached. The only thing that actually will coincide is the connection between those two different node languages. But whatever you are creating in one language can be fully created, deleted, updated, reordered and everything in that second language. So you can literally have a text block or an image in one language that you have nowhere in the translation. And that actually created a lot of challenges for us because what happens when you start to diverge, you go away from your entire process, so to speak. So what I just mentioned here, I'll skip over this one. The symmetrical approach, however, is the one that we took, which is we are going to keep things in the same order. We're going to keep things tightly coordinated between the original language and the translation language. So here is, for example, just a very basic page that I threw in in the layout builder. The title is in the upper. You've got a text paragraph on the left. You have an image paragraph on the right. And below is just a listing, basically. As you can see, this is the default in English, so the listing is, for example, automatically pulling the English version of whatever content I have. So the relationship is going with the same language. The image, you can see that I'm loading the English version of the image that I'm referencing. The text paragraph is, of course, in English. There is a module as well. We're using it. Please follow the links because you can always look it up better there. So when I look at the elements, you can see in the lower left corner the teaser image that I was using. That one, I can edit it in the original language. I'm in the original, the English language. When I'm actually looking at the German translation of it, you can see that the teaser image is not there because actually it's set. I can only edit it in the original language. If I want to edit it, if I want to delete it and add a different picture, I have to go to the original language and replace it so I am forced to use the exact same image in the original as in the translation. That can create some issues, but at the same time, it allows us to keep that tight coupling a symmetrical approach. The same thing goes for the layout builder. As you can see where I've got the arrows, you have the elements for creating, deleting, updating, as well as reordering. So you can reorder everything, but this only is allowed in the English language, in the original language. I mean, when I go to the translation, those things are not allowed. As you can see there, I do not have the buttons for the creating and deleting or the reordering. I do have the ability however to edit. So when I want to edit anything, for example, this image again on the right hand side, it opens up the editing panel. However, I can only change certain elements like the text itself. I can translate it. So one thing that I do not have on these images but is very important is this creates the situation that when I want to add a new block to my page, I actually have to go in, add that block to the original language and that block itself, the image or the text or whatever, that is automatically added to all languages. And that becomes a very big disadvantage because for the moment, I have published online a block of text that's in English, but it's showing up on all the German or the German translation as well. So I have to be very quick if I want to be professional about it and then translate that very fast. So that's the one big disadvantage to our approach in that regards. Good. Once again, appearing in all of their languages. I'm actually going to skip over the next few slides because they were more from the coder perspective and that's not actually the intent for today. But you can certainly come up and ask me about more of the coding that we've done or the distribution that we've done so I can give you more of an insight for that afterwards. I left them in here however because of the fact that they were helpful to other people. So just doing the language prefix, the changes to the language path, everything like that. So within our distribution as well as the work that we are doing, we've actually taken a lot of time to do things like hiding of those untranslated fields. For example, the image references and stuff. We actually streamline the process for translations in a symmetrical way. We also have taken a lot of time to do things like developing the language switcher itself. So we've got actually a kickstart that's public for our front end that will manage the language switcher and working with meditakes and things like that. If you want more information, those links that I gave you beforehand, please use those or there's also the stack.lupus.digital which we've got up as well. But really go to thedrupal.org, the decoupled link that I had showed you earlier because that one will be probably the most helpful for you. Once again, thank you very much. My name is Jeremy Jinkwist. I'm actually with the Drupal Austria Club and I'm the cashier there. So we had a lot of fun putting on Drupal Dev Days earlier this year. Hope you can come up and talk to me about that. My colleague again is Leopold Novelli. He also is very enthusiastic for open source technology where he actually has a radio show in Slovenia. He's actually done things like interviewed the Minister of Information for Slovenia, which is really cool. Thank you very much. I think we have a few minutes for questions. Yeah, correct. Yeah, it's incorrect. True. I will one second. I just have to repeat it first. So you were saying that for images, in this case what I've got up here, you are loading the information that's in English, the caption and the other. For screen readers, that's actually a really bad thing. So how do we address this problem? Okay. As you can actually see here, here is the image paragraph that we are loading. The image paragraph has not only the image file itself, but it also has the caption information, the description, etc., and the link. So these things on the right side are actually editable in each language. I can change the capture. I can translate that. I can actually translate the link, the description, etc. But I'm being forced in this instance to keep the same image file. And so I achieve my goal of having it translated as much as I can, but we are not allowing for divergence of this image paragraph. It is actually a media entity. Yeah. Okay, so the question was why don't we make it an image entity from the media library, I assume? And if that is the case, then we were able to load the German translation. Unfortunately, I'm not involved as much in the code in that regards. I'm not sure what was preventing us, but we had decided to go with this route that we have the information translatable here from the paragraph itself. In the media entity, it would certainly be possible. I'm just not sure what the blocking feature was. But yeah, if technology were perfect, that would be great. Then thank you very much and I'm available.


Hi, we are discussing numerical methods for capturing isolated roots for non-linear equations. In today's class, we will extend our studies to system of equations. We will restrict our discussion only to system of two equations. Once we understand this, extending the idea to any number of equations is straight forward. So, with that in mind, let us consider two non-linear equations given by f 1 of x 1 comma x 2 equal to 0 and f 2 of x 1 comma x 2 equal to 0, where f 1 and f 2 are functions from r 2 to r, right. We can write this system in the vector notation as f of x equal to 0, 0 is vector and f is given by f 1 comma f 2, right and x is the vector in r 2 and f is a function from r 2 to r 2. Now, we are interested in finding an isolated root of this non-linear system. Let us call this isolated root that we are interested in as the vector x star and it is given by x 1 star and x 2 star. Remember, right from our chapter on numerical linear algebra, we always considered vectors as column vectors that is why whenever I write a vector, I write it in the row wise and then put a t there. It means it is written in the column wise. I am doing this just to save the space. If I write it in the column wise, it may take more space, right. So, you should understand the vector for instance this as x 1 star and x 2 star. This is what we meant by writing like this and putting a transpose here. The idea is to first set up a fixed point iteration sequence. If you recall in our last two lectures, we have introduced this general framework of iterative methods with one initial guess in the form of a fixed point iterative method. So, we will apply that idea component wise to each equation in our system and thereby, we have two equations. In the vector notation, this fixed point iteration method can be written like this where G is the vector valued function from R 2 to R 2 and x n is a vector in R 2 and this expression generates the iterative sequence. We will provide the value of x naught as the initial guess and then we will generate this sequence using this expression for x 1, x 2, x 3 and so on. Remember the function G is called the iterative function and this has to be specified as the part of our method itself. All these ideas are familiar to us therefore, I will not explain them once again. Now, to analyze the convergence of this fixed point iteration method, if you recall we have certain hypothesis proved in our last class when we worked with single non-linear equation. The same idea will also go with system of equations. Recall that you have this system f of x equal to 0, you will write it in an equivalent form as x is equal to G of x that is the main idea of the fixed point method. So, you will choose this iteration function in such a way that isolated root of the non-linear system f of x equal to 0 is also an isolated fixed point of the iterative function G. Therefore, we will denote the isolated fixed point of G as x star. Now, we will use the Taylor approximation to write each component of the vector G around an iteration vector x n with Taylor polynomial being degree 0. Then the reminder term is given like this. Remember this is the Taylor formula in two dimension. You should go back and recall how we write Taylor's formula in 2D. We have only introduced it for one variable. You can similarly write the Taylor formula for two variable functions. Here I am just writing the function G at the fixed point and that is taken around the point x n and we have only taken the Taylor polynomial of degree 0 and therefore, the reminder term is written like this. Here you will get two xi n's one for each component that is for G 1 when you expand you will have a xi 1 and since we are expanding this G around the point x n therefore, we will also use the notation xi n for it and this is a vector and it is given by xi 1 comma n and this is for the first component of the vector G and xi 2 n and this lies on the line segment joining x star and x n. Remember you are writing G at x star and using the Taylor formula at a is equal to x n that is what you are doing and the Taylor formula is written with polynomial of degree 0 that is Taylor polynomial of degree 0 and you have the reminder term. So, you have to do it component wise we have two components for G. G 1 will give one such expression and G 2 similarly will give another expression like this with xi n of 2 now equal to xi 1 n of 2 comma xi 2 n of 2. This is the notation that we will use now you can see that this is equal to x 1 star right this is what we have given here G is chosen in such a way that x star is a fixed point. Therefore, this is equal to well xi for i equal to 1 G 1 of this is x 1 star and G 2 of this is equal to x 2 star that is what we have written here. Similarly using the iteration formula you can write this as x i comma n plus 1 right and then I will take this to the other side to write x i star which is on the left hand side minus x i n plus 1 which I have taken from the right hand side to the left hand side and that is going to be equal to the reminder term that is already there on the right hand side right. So, that is what we get here and this is obtained component wise that is i equal to 1 and 2. Just to write these two equations in the matrix form we get this equation I am just putting i equal to 1 and that gives me the first row of the system and put i equal to 2 that gives me the second row of the system ok. So, now we got this now we will give a notation for this matrix remember this is nothing, but x star vector minus x n right and this I will give a notation g n therefore, this will be g n into x star minus x n sorry this is x n plus 1. So, this is what we can write it in the vector notation for that I will define the matrix g n like this. Now, what is this g n if you recall the Jacobian of the function g remember g is a vector valued function right therefore, you can write the Jacobian matrix of g and it is given like this. Now, this is not exactly the Jacobian matrix because for having the Jacobian matrix you have x applied in all the elements of this matrix whereas, here we are applying xi 1 for the first row this is also xi 1 and this is actually xi 2. So, this g n actually resembles the Jacobian matrix of g, but it is not exactly g, but one interesting thing that we can observe here is as n tends to infinity if your sequence x n converges to say x star then you can see that xi n 1 will also converges to x star and xi n 2 will also converges to x star. Why it is so? You can see that xi n 1 and 2 are lying on the line segment of x n and x star right. So, that is what we have seen when we were expanding g in the Taylor formula therefore, as x n tends to x star by the sandwich theorem you can see that xi n will also converges to x star. Therefore, in the limiting case everybody will have x star as the argument that is all the elements of this matrix will be evaluated at x star in the limiting case right. So, in the limiting case this g n will be precisely the Jacobian of the matrix small g evaluated at the fixed point x star of this function g. And as I told in the previous slide we can write our equation in the vector notation like this remember this is the error vector at the n plus 1th iteration that is equal to g n into E n. Remember this is a matrix and here you see this is a matrix and this is a vector. Therefore, the right hand side is the product of matrix and vector and that is actually a vector. Now to see the convergence of the iterative method we have to take the norm of this equation on both sides and then we have to see how this matrix behaves right. Let us state the convergence theorem of the fixed point method for a system and we will omit the proof of this theorem. The theorem says that let D be a closed bounded and a convex set in R 2. So, if you recall what is mean by a convex set by convex set we mean that the set D should be in such a way that you take any two points in the set D and draw the line segment joining these two points that line segment should entirely lie in that set and this should happen for any pair of points right. So, suppose if you take a set like this this is not convex because if you take two points like this and draw the line segment that line segment will not entirely lie in the set D. So, this is used in the proof of this theorem that is why we are assuming anyway we will omit the proof for this course. The second assumption is that we will assume all the components of the vector G are as continuously differentiable functions at all the points in the domain D and further we assume that the iteration function G is a self map. If you recall we now know why we are assuming all this conditions on G at least in the case of single non-linear equation we have studied all these properties in full details and then if you take the maximum of the matrix norm remember this is the subordinate matrix norm and we are just restricting it to the L infinity norm that does not matter you can use any norm for easy handling in the proof it is better to have the L infinity norm that is why we have taken this and if you take the maximum of the L infinity norm of G then that should be less than 1 remember this is the contraction condition right. Then the theorem says that G has a unique fixed point in the domain D remember the existing existence comes from the continuity of the function G and the self map and the uniqueness comes from the assumption that G is a contraction map. Then for any initial condition x naught in D that is if you start your iteration by taking x naught in the domain D then the iteration sequence x n will be well defined and all the terms of the iterative sequence will lie in the domain D and further x n will converge to the fixed point x star in D and further we also have this estimate which tells us the order of convergence of this fixed point iteration method is actually 1 that is it has a linear order of convergence right. So, you just keep your knowledge that you had in the case of single non-linear equation and just see this it is only the vector notation, but idea is the same as we have studied in the case of single non-linear equation. However, proof will use some multivariable calculus ideas therefore, we will omit the proof of this theorem. Now the question is can we improve the order of convergence by suitably choosing our iterative function G. Again if you recall we have done such an exercise in the case of single non-linear equation. Again the idea goes very much similar to that let us see we will now see how to choose G for a given system of non-linear equation. So, as to faster the convergence for that we will now take G that is our iteration function as x plus a into f of x and look for the fixed point of this function. So, this is your G of x and you are looking for the fixed point of G of x that is you are looking for the root of this non-linear equation where a is a matrix that needs to be determined in order to faster the convergence. If you recall how can we make a faster convergence in the single equation let me quickly recall that we had limit n tends to infinity mod x n minus x star this is the fixed point divided by mod x n minus 1 may be we will put plus 1 here x n minus x star is equal to G dash of x star that is what we have obtained. Now in order to have higher order convergence here we need to choose G such that G dash of x star is equal to G dash of x star 0 that is the idea the same idea here instead of G dash in the single equation. Now we will have the Jacobian of the vector valued function G. So, that is the only difference that we will have in our present case. Let us see we will find the Jacobian of this iterative function and see how it looks like you can see that the Jacobian of this function is G of x and it is given by the n cross n identity matrix i plus a into f of x where f is the Jacobian of the function small f of x. So, that is how the Jacobian will look like and if you go back recall that the Jacobian of the function f of x is given by this matrix right. Now how to get the faster convergence precisely we have to look for that iterative function G such that this is equal to 0 that is the idea which is similar to what we had in the single equation case right. So, therefore, we will look for the iteration function small g such that norm of G n infinity is equal to 0. Let us try to achieve that for our initial guess x naught. Now how you will get remember G of x naught is given as i plus a into f of x naught right. Now we want norm of this to be equal to 0 that should be the case when the matrix itself is the 0 matrix. Remember this is one of the conditions of the matrix norm right. So, I am just using that in order to have the matrix norm remember this is the subordinate matrix norm ok. So, in order to have the matrix norm equal to 0 I should have my matrix itself as 0. So, if this matrix has to be 0 it means my a should be equal to minus f of x naught inverse right. So, that is how I will get this expression to be 0. So, therefore, in order to have this which will actually make my fixed point iteration sequence to have a higher order of convergence in order to have this I need to choose my a as minus f of x inverse and this I will do for each iteration that is I will propose my a just to have the notation a n here because I am going to change my a in every iteration. Therefore, I will have a n which is defined as minus f of x n inverse where capital F is the Jacobian of the victor valued function small f. Therefore, my actual iteration formula that is fixed point iteration formula is given like this. Remember we have taken it as x n plus 1 equal to x n plus a into f of x n right and now I have taken a as this expression. Therefore, this is my iteration formula given x naught now I can generate my iteration formula for n equal to 0 which gives me x 1 n equal to 1 that gives me x 2 and so on. You can just see that this is very much similar to what we defined as Newton-Raphson method in the case of single non-linear equation right. In the case of single non-linear equation the Newton-Raphson method looks like this x n minus f of x n divided by f dash of x n and this seems to be a natural extension of this formula to a system of non-linear equation and that is why this method is called Newton's method. Let us do an example consider this system of equations and we are interested in finding an isolated root of this system for that we will use the Newton's method with x naught given by this vector. As a first step we have to compute f of x inverse right because that is involved in our formula.  Therefore, the Jacobian of this function small f is given by this formula and now f 1 is given like this and f 2 is given like this from there you can compute each of the elements of this matrix and they are given like this right. So, we found f that is capital F now we have to find the inverse of that matrix and that is given like this. Once you find the inverse of the Jacobian matrix capital F you can now go to set up your formula for the Newton's iteration. Now for each x n therefore, you have to find this matrix for x naught the matrix is given like this. Therefore, to compute x 1 which is component wise written like this and that is given by x naught which is this into f of x naught inverse right. So, remember this is obtained from the inverse of the Jacobian matrix times f of x naught. So, that is what is this and therefore, the first iteration formula is given like this. Now once you have this idea you can compute your x 1 and that is given like this. Now once you have x 1 you then have to find f of x 1 once you find this matrix then you have to find the inverse of that. Once you find the inverse of that then you can set the expression for x 2 that is given by x 1 minus this inverse matrix into the vector f of x 1 right. Like that you can keep on going as long as you want to go right. So, this is how we can implement the Newton's method for a system of two equations. Let us take a small application of this Newton's method. Here we would like to find an extremum for the given real valued function f defined on R n. So, this is what is called the unconstrained optimization problem. We will assume that the function f is continuous function and recall that a point x star is called a stick to local minimum. Similarly, you can also define for local maximum. A point x star is called a stick to local minimum of f if f of x is greater than f of x star. Suppose you have the function like this just I am imagining it in the case of a I am just showing it in the case of a function in R then this is a local maximum and this is a local minimum and this is local maximum and so on right. Because you just have to have this condition in a small neighborhood of x star. Suppose this is your x star then you can see that in a small neighborhood of this x star this is the maximum right. So, therefore this is a local maximum and similarly you can see that this is a local minimum and so on. So, similarly you can also define what is mean by local maximum. Now from the calculus course you can see that a necessary condition for x star to be a stick to local minimum or maximum is that this partial derivative should be 0 right. Thus we have to set a non-linear system of equation like this. So, that an isolated root of this system will be a local maximum or minimum of the given function. So, let me write it in the vector notation if you see this gives you the gradient vector right. Therefore I am writing my non-linear system as gradient of f of x equal to 0 vector where the gradient is given like this. This is precisely what I am writing this system in the vector notation. Now we have to find an isolated root of this system for that we can use the Newton's method to obtain an approximation to it. And the Newton's method is given by this formula where H is the Hersian matrix for the function f right. If you recall in our first discussion we had a vector f that is the function from R 2 to R 2 and we had Jacobian of this and H is the function its inverse is used in the Newton-Raphson method. Now what we are doing is there is a slight confusion in the notation that we are still using the notation f now which is a function from R 2 to R and we want to find a local maximum or minimum for this function. For that what we are doing is we are setting up the system grad f equal to 0. So, that is what in the unconstrained optimization we are doing. In unconstrained optimization we are given a real valued function defined on R 2 in general it can be R n and then to find the local maximum or minimum of this function we have to set this non-linear equation. Therefore you have to apply the Newton-Raphson method for this equation just like how you applied the Newton-Raphson method for this equation f of x equal to 0 in our previous discussion. Similarly you have to now apply this Newton-Raphson method for this equation and therefore you have to find the Jacobian of grad f. Jacobian of grad f is nothing, but the Hessian matrix of your given function f. So, that is why we are having this and that is given by this formula. So, once you have the Hessian matrix then you know how to set up the Newton's method iterative sequence and it is given like this. Just follow the Newton's method that we have introduced in our previous slide. Note that if x star is a stick to local minimum of f then the Taylor formula can be used to show that the Hessian matrix is non-singular. Therefore you can always invert this matrix and therefore h is non-singular in a small neighborhood of x star and therefore you can always invert this matrix right. Again let us quickly see an example. Now we are given this function this is a real valued function defined on R 2. Now we want to find a local maximum or minimum we will call it as local extremum of this function. For that first you have to set up your non-linear equation for that you have to find the gradient of this function f and it is given like this. Therefore you have to set up the Newton's iterative formula for this system right. So, you have to find the Jacobian of this vector and that will be the Herschian of your given function f right and that is given by this matrix. Once you have this you can find the inverse of this matrix and that is given like this. Once you have the inverse of the Hessian matrix you can set up the Newton's method and that is given like this. Now once you have this then you can start with the initial guess and you can go on computing the Newton's iterative sequence and if that sequence converges it will converge to an local extremum of the given function f of x 1 comma x 2 equal to this expression. So, that is the idea with this our discussion on non-linear equation is complete I thank you for your attention.


practices are due to the local conditions and we had left with looking at the effect of changing environment because of the irrigation coming up in that area that at the time when we are collecting the data the micro environment or the micro climate was different than the climate which has been obtained after the project has come into picture. And we have seen that the through one example that whenever there is a dry condition whenever there is a condition where you have arid climate, semi arid climate and you have the areas irrigated areas surrounded by the fallow areas which are dry areas which are not irrigated areas then you will have the the advection effect, the advection will be uhh experienced and because of that you will have the conditions looking at the general wind direction. Now if you look at the windward side the starting edge of the the windward uhh uhh side of the field will have the cloth line effect whereas subsequent to that you will have the oasis effect. The case of oasis effect what it means? It means that the the conditions have become such that the evapotranspiration has reduced because of the fact that the air mass which has which has passed over the or which is passing over the irrigated area is is becoming cooler and is becoming more humid. So because of that its its capacity to evaporate or its uhh capacity to evaporate will reduce and therefore we have also looked at that as a correction you will find that if your if your areas are very large the irrigated areas are very large the net effect will be that you will have to put a correction factor which is less than 1 because of the the enhanced oasis effect. So that will be the end result that will be the end result uhh in terms of reduced value of evapotranspiration than what you have observed when the conditions were uhh such that you were you were using the data on small patches of irrigated areas which were surrounded by or which were followed by the the the the the follow areas or the areas which are not irrigated. So that will make a difference of may be 5 to 10 percent and you can put a correction factor on the the crop coefficient. Let us look at some other other effects uhh which can be which can be taken into consideration the effect due to the soil water. The level of uhh available moisture or the level of moisture which is prevalent at a particular time that will also influence the evapotranspiration activity and that is what is shown here that it also depends on what is the what is the condition of the climate. The climatic conditions will also influence but assuming that the climatic conditions are uhh not very different than the factor which is influencing the other factor which is influencing the 80 crop will be that what is the what is the type of soil. For example if we if we assume that we know the type of soil because ultimately the the moisture holding capacity or the way the moisture is held is a function of the soil characteristics as well. So if we if we assume that the soil characteristics are known then we we know by now that the moisture depletion or the moisture deficit which is being created up to a particular level you might be in a position the the root system might be in a position to extract the moisture without any problem but when the the tension increases then the evapotranspiration activity will also be affected. In general the 80 crop is not affected up to a stage where the atmospheric tension is close to 1 atmosphere and at that stage there is a stage for different soil types for example in the case of clay that stage will be attained when you when you reach a level of 30 percent of total available water, kw is total available water and in the case of loam this level of 1 atmosphere will approach at a station where you have extracted around 40 percent of the total available water and in the case of sand up to around 60 percent of the total available water. So these are the indicators these are the indicative one you you will at least you can now visualize that how much moisture is available in in fact without influencing the the evapotranspiration characteristics or without reducing the evapotranspiration in a particular crop. Let us have a look at this variation on some actual case where so if you mean 80 cotton millimetres per day this mean 80 cotton is between the period between the irrigations what is the mean value of evapotranspiration? On this side if you irrigation interval let us say that we have the irrigation interval varying from these values and so on and on this side the scale is sometime something around. How the irrigation interval influences the 80 crop? In other words what we are saying is that if you are applying the water more frequently then what will be the effect on the 80 crop then if you will apply the water at a larger interval. So for example in this particular case it has been observed that when you are applying the water uhh 80 cotton is 6 millimetres per day. As long as you are applying the water at a reasonably large interval also it is not making much effect only after uhh if you go beyond interval of around 18 days there is making some impact on the 80 crop whereas if this evapotranspiration is other extreme you might find that in this particular case might be having something of this nature. Even if since the evapotranspiration level is very high even if you apply the water very frequently you will find that in general the if you would have applied the water at the desired rate then the evapotranspiration, the potential evapotranspiration could have been 14 and there is a maximum which it there is a peak consumptive use rate of the peak evapotranspiration whereas because of the fact that you are applying the irrigation at a longer intervals the evapotranspiration the actual evapotranspiration has reduced. So you also know by now that the evapotranspiration is directly related with the the ultimate yield of the crop if if the crop is not in a position to evaporate uhh or evapotranspire at the desired rate it will have the impact on the ultimate yield, okay. So in in this situation your yield will be affected if you are not supplying the moisture at the proper rate similarly in the in the intermediate situations you will find a similar effect that the effect might not be as much as in the case of a situation where your evapotranspiration was very high. The is is basically the rate at which the deficit is being created that is going to influence what is the rate at which you must replenish that deficit, so that is what is depicted in this particular case and for the other cases also it will be slightly more but again there is some impact which which shows that we are we are trying to basically bring in uhh some other uhh factors that when we go in for the designs we have to ensure that we we know these relationships we know what is the impact of delay in the moisture supply on the drop yield and those things will have to be incorporated. Those things will have to be looked into for proper management of water. Now as far as in this particular situation uhh depending on uhh the the the actual level of your evapotranspiration the factor which has to be incorporated will be dependent on what is the what is the actual practice you are adopting, what is the actual uhh irrigation interval which you are taking into consideration and on that basis you can you can incorporate the the effect or the correction factor on the the Kc values, okay. The Kc values will also be influenced if your evapotranspiration is not take place at the at the desired rate that is what is happening here in this case that is very very essential to understand that if you are supplying the moisture at the rate which is the desired rate in this case this is the desired rate then you are you should have been in a position to get the evapotranspiration at the same rate but since you are applying the irrigation at at higher intervals in other words what is what is happening is that you know this is your the total available moisture, total available water out of this you can only only this much can be extracted this is what can be extracted by the the crop system without any ET crop is not it. So if you if you keep this much moisture in the soil then the ET crop will occur at the potential rate. If you reduce now what happens when I supply the moisture at a at a larger irrigation interval the irrigation interval means that you are supplying you are replenishing this deficit which has been created if if it takes it takes 5 days to bring down this moisture level to this level which is the level where up to which you do not have any effect on the ET crop if it takes 5 days if I wait for 3 more days if I make the interval 8 days then this soil is not having that much capacity to absorb the moisture to be serving the plant for 8 days and that 8 days limit is on the basis of what is the rate at which the moisture is getting depleted that is the ET crop that is dependent on ET crop. So if your ET crop is high it will mean that you will have to replenish the deficit which is created the deficit will be created in a relatively smaller period and unless you replenish that deficit after those many days you are going to have problems your unit is going to be affected. We will come back to these all these concepts later also when we will go into the scheduling at this stage I think this much is sufficient to know that all these are the additional factors but at the same time let me let me point out at this stage that these factors which we are discussing the local factors or the factors which are dependent on the local conditions as well as the agricultural practices this is not going to influence very drastically the ET crop the the percentage up to which this might be influenced unless there are some specific very specialized conditions you will find that the percentage will be the order of magnitude will be around 5 to 15 percent but the same time in some situations it becomes quite very major factors and there can be a situation where it can be ready detrimental if you are not taking care of the these impacts. Let us now go to the ground water ground water is another condition which will influence the the KC values or you can also say that it will influence the evapotranspiration activity why because in the case of the ground water the level at which the ground water is available if you have if this is your ground water is somewhere in this at this level this is the ground water level depends what is the what is the depth ground water is in comparison to the ground level it also depends on which crop you are growing what is the the the root system what is the effective root zone so if the effective root zone is this much in some cases it might not influence the crop that case is dependent on the soil type because how much how much this ground water influence this zone is the function of the capillary characteristics of the soil. So in some cases if the soil is is a light soil the soil is sandy then the situation is not that bad in that situation the capillary zone will be very small and you might not you might feel that in this particular case if the ground water is somewhere here it might not influence the root zone whereas if you have the heavy soil it will influence the root zone but in what way the this ground water in what way it influences the evapotranspiration there are various items which will one is that you will have the soil in this area will be its water content will be higher will be wet soil and that can create problem in terms of the agricultural operations for example if you want to use the the land the land preparation if the water content is very high the land preparation cannot be done very well because you cannot you cannot do many operations on the soil if it is very wet the water content is very high. Secondly you will also find that the wet soils they they do not even under the the conditions when the energy is available they get warm very slowly. So because of the slow warming you will find that the delayed germination will be there because for the germination to take place the the temperature in the soil has to reach a particular level. So there can be delay in the germination and preparation is another situation where you are having problem in terms of the ground water availability. The prompt plant development can also be delayed these are some of the factors along with this you will also find that there can be problems due to the variation if the water is if the moisture is always available in the soil at the ground water level the ground water table is quite close you will find that the pore spaces will be always filled up with water and the aeration can be a problem. There are if you look at the crops there are many crops which behave differently under these conditions of high ground water availability and they have been divided into the three different categories those crops which are high tolerance towards the ground water, medium tolerance and those which are sensitive crops. The ground water is at 50 centimetres these are the crops which are having high tolerance sugarcane potatoes broad beans and the medium tolerance crops are sugar beet, wheat, barley, oats, cotton, sensitive crops are maize and tobacco. Similarly under the waterlogged conditions the waterlogging conditions means that the ground water is even still higher under those conditions the rice will have strawberries, grasses most of the grasses plants these are the high tolerance crops whereas the other extreme is the peaches, cherries, olives, peas, beans. So the characteristics of the crops will have to be looked into when you have these situations where the ground water is very high is quite close to the root zone and as I have told you that is also going to be a function of which soil you are dealing with. So in this case here the minimum depth of ground water table this is a general thumb rule which has been suggested here if you have sent any soils the rooting system or the root zone depth plus around 20 centimetres is the recommended depth up to which the ground water table should be beyond that in the case of loamy soils plus 40 centimetres in the case of clay soils plus 80 centimetres. If you have these conditions prevailing then in general you do not have to put any correction factor. If your conditions are violated then you will have to look into the greater depth which crop you are talking about how much it will be influenced because of the close proximity of the ground water table and that effect has to be taken into account. Item which we like to look at is salinity. Salinity affects the evapotranspiration activity in many ways one is that it exerts osmotic pressure. So because of this the root system will find it very difficult to extract the moisture. The salts which are available their osmotic pressure is much higher and that will create the conditions where the levels which you are discussing which we are saying that in a particular soil the level of extraction by the root system we have defined those levels those levels would not be valid anymore if you have the saline conditions then it will also affect the physical characteristics of the soil. The structure of the soil can be affected it will also cause toxicity and affect the growth. This toxic conditions can be harmful to the crop development and salinity can from that angle it can influence the crops and once the crops are influenced then you have the influence on the evapotranspiration acts as well. One way to offset this particular situation is to keep the level of moisture which is available at any time in the soil at a higher level. With the high moisture levels these effects are reduced. So there is one way of handling that situation then there are other ways by reducing the salinity or by even doing the leaching process. Leaching is the process in which you use lot of water to flush the salts which are harmful salts from the soil to a level much lower than the root zone system or the root zone depth. So you apply lot of additional water on the surface and that water dissolves the salts which are which are the problematic salts. Those salts are taken to a level in that case the groundwater table has to be much lower and in case where you have water logging problems you cannot do that. But in those areas where the rainfall is quite high the leaching is automatically done whenever you get lot of rainfall that is is being the leaching process in a natural manner but in those situations where the rainfall is not excessive you might have to use the rainfall the irrigation water sorry the irrigation water not the rainfall you have to use the additional irrigation water and that becomes the additional requirement of irrigation is known as leaching requirement which will again when we look at the total requirement when we consolidate the requirements of irrigation we will come to that leaching requirement also but that is one way of reducing the salinity but in general the ETC value or the crop rubber transpiration is not chained unless you are certain that the salinity is creating a problem or is creating some effect on the growth of the plant. So unless the growth is affected if there is some level of salinity you might ignore that there is no connection which is made on the KC value, correction is required only when the the level is such that it affects the growth of the water and crop yield. This is another aspect which we have to understand then the crop production the timing and duration of water shortages we have slightly discussed in the earlier part when we were looking at the soil water availability. This concept was this protein that when you are making the water available at what time you are making the water available and how much you are making that water available those two things are going to decide what is going to be the crop yield ultimately. There are situations where the deficit which is being created in the soil the timing of that deficit is also very important because of the fact that the growth stages of the crop there are some sensitive growth stages than the other stages which are which are less sensitive. So if you create a deficit in a stage which is less sensitive it might not have very detrimental effect on the ultimate yield than the other situation where the growth stage is very sensitive and if the deficit or if the conditions are deficit conditions at during that stage if that happens then you are going to have problem then the impact on the ultimate yield is going to be much larger. That is shown on the using the actual data let us plot actual data of this is from non forage that is between yield as percentage of maximum yield that means 0 to 100 percent what is the actual yield as percentage of the maximum yield which can be achieved in that crop. On this side is the ratio of actual 80 crop maximum 80 crop. The maximum 80 crop is that situation where which will be attained when you are supplying the moisture as much as is required. So if you plot this for non forage crop plot it some this is the variation now this area this plot is a plot which is showing the mean variation which suggests that if your actual 80 if your actual evapotranspiration reduces then the yield will also be reduced accordingly and the yield reduction is in this particular case the yield reduction is looking to be proportional but is not always so it depends on many of the factors it depends on where those deficits are created in the total growth period of the crop. This dotted portion is showing the variation that in general for different types of deficits for example if you had created the deficit in a stage which was very sensitive stage then in that case you might find that even if you had created a deficit which was not very high deficit but the the impact which it made on the ultimate yield was very high in this case but look at this for example let us say that if you are somewhere here now your deficit creation is the actual 80 is quite close to the 100 percent level but still the amount of yield reduction which has which it has done it might be quite large in comparison to the other situation example if you are somewhere here this is the the yield percent as percentage of the maximum it has reduced by around 50 percent whereas if the stage was some other stage the same thing has been found that there is hardly any impact on the yield for example if the if you are looking at this extreme of the the graph you find that there is hardly any any difference in the the yield when the same deficit was created in another stage so this variation this scatter of this total area which has been shown here that proves that point that is not only the deficit the level of deficit which is important but is also important that that at which stage that deficit was prevailing similarly for some other crops also for example in the case of sugarcane the plot is something of this nature scatter is this is the same both the scales are same and on this side is the ratio of the the actuality to maximity and this side is the the yield as percentage of yield maximum yield. If you look at this this particular area belongs to the the situation where you have created this deficit in the lead growth period and this side when the deficit is created in the actual if you are creating any deficit in this period which is more sensitive period than the the lead growth period then you are getting more for the same for the same level of 80 reduction you are getting less amount of yield or the yield reduction is much lower this area of relationship between the crop and the yield reduction is a very vast area and it has been treated separately in another of your paper, paper number 33 the yield response to water so that is a very elaborate explanation on all these factors how this yield reduction is taking place and what are the various characteristics of the crops on which it is based on. Let us come to the other factors other conditions which can influence the the ET crop and what is the method of irrigation? Which method of irrigation you are using? They will also make some impact on what is the the evapotranspiration or what is the influence on Kc value and what way this can this can influence the Kc? Again the the the major factor which will influence is the way the moisture is being made available because these methods so far we have not discussed what are the various methods of irrigation we will be very soon discussing those but in general to tell you that there are methods which are known as surface irrigation methods which use the concept of the gravity flow and sometime they are also termed as flooding method that there can be some change in nomenclature but what we mean by that flooding is that you are making the water available on one side of the field and it flows under the gravity force to the the downstream side of the field then there are methods like sprinkler irrigation method to use the sprinklers and the water is sprinkled over the the area in which case it will wet the plants also whereas in the case of surface irrigation method the that irrigation those irrigation methods would not wet the the foliage of the plant the canopy would not be touched even. Then you have the drip irrigation method in that case you are using the drippers and you are you are making the area which is providing the moisture to the the root system you are making that area reduction in the the moisture requirement can be made so these are the major these are the major methods now in these all these methods has been found that ultimately these methods do not make much difference in terms of the the evapotranspiration requirements unless they are in in some case for example in the case of surface irrigation methods since you are wetting the total soil is felt that it might be more water consuming method but is not so because in the case of sprinkler irrigation you might be reducing the amount of moisture which which has to be supplied on to the the the area or you might be in a position to have a better control on the irrigation method because you can operate the system anytime you feel like you can operate it for any period of time as desirable whereas in these methods you cannot do that because there is a requirement that the water must flow from the upstream end to the downstream end and that requirement has to be fulfilled so as to provide a uniform depth over the whole length of the field but in this situation since we are putting the water from the top the the crops get wet and it enhances the evaporation the evaporation is much larger all that water which remains on the the leaves that gets evaporated the evaporation losses increase then there are some losses which are spray losses which are because the wind the water might go to some other areas where is not intended to be applied on so that can be another loss in in top of the total requirement that requirement remains almost similar. There can be some saving in the case of drip irrigation methods so from these point of views the method of irrigation can make some difference but not very drastic difference you have to look at the other conditions other prevailing conditions if you are looking at the sprinkler irrigation how much is the the wind influencing the irrigation activity so all those things have to be incorporated and that is what I think at this state we can only just mention about those those variations because of the irrigation method. Then the cultural practices these can also influence this plant population tillage mulching and the provision of wind breaks in the case of fertilizer it will only influence the evapotranspiration if the salt the desired salts in the soil are not available so if in that situation unless you supply the fertilizer unless you apply the fertilizer from outside as additional nutrition which is desirable or which is required it may not have any impact because if the natural salts are available then the fertilizer might not have any impact. So you have to look at what was the condition of the soils with respect to the condition of the soil only you have to look at these this particular factor. You can also to certain extent in even now consider where the salts are where these salts are available are these available beyond the root zone depth or they are within the root zone depth or are you is your irrigation method such that is flushing the salts beyond the root zone depth or even if you have supplied the fertilizer is it flushing the fertilizer beyond the root zone depth if that is happening then that means there is some is going to affect the evapotranspiration activity. So only from that angle that since it is affecting the crop growth it might affect the root zone the evapotranspiration activity as well. And the plant population is not a very major factor it will make some difference in terms of the evaporation because if the plant density is high then the crop will cover the ground and only in the beginning when is the initial stage you will find that evaporation will be influenced to certain extent but in the later on stage when the crop coverage is going to be there anyway there is not going to make that difference also in the evaporation activity. So the evaporation activity is the major activity which is going to be the evaporation from the soil is going to be influenced in this particular situation. The tillage is the process in which you just disturb the top soil for various reasons one is the weed control you want the weed to be removed the other is to change the soil structure 3 times the soil gets sealed the top soil gets sealed because of the impact of the rain drops and that sealing process will change the structure it might seal the pores and that sealing process will influence the infiltration ultimately and since the influence the influence of infiltration will be to reduce the moisture getting absorbed into the soil more of the water which is going over the soil will be going as a waste as a runoff very little amount will be in a position to go into the get into the soil and thereby get absorbed. So from that angle tillage can make some difference if it is rough weed around and if going in for the tillage practice you might be able to influence the weed and thereby reduce the evapotranspiration. Similarly the mulching in many situations people feel that through the mulching what is mulching first of all mulching is the process in which you let the waste the crop waste be into the soil and remain there so that it can it can influence the things like the rain drop impact can be reduced you also want in some cases to reduce the evaporation from the soil but it has been found that ultimately there are some advantages of mulching but there are at the same time some disadvantages also it is not always true that through the mulching you will get the desired effects which you thought you will be getting for example the disadvantage one of the major disadvantages that it creates the similar problems like the close proximity of groundwater it will make the soil remain wet most of the time it will also induce many diseases those can be because of the mulching and because of the additional foliage being made available on the top of the soil so that can be there can be some impact of mulching it can be taken into consideration wind breaks can also be influencing the the ET crop it has been found that the wind breaks there is a there is a thumb rule that the height of the wind break which is being used will be deciding how much will be the influence of the wind break in the windward direction up to which extent it can influence is around 25 times the height of the wind barrier that wind barrier can be in the form of trees or it can be some artificial wind barrier also but the influence is something of the similar nature that assuming that if you are providing the wind barrier what it is doing the other climate it cannot change it can only change the the wind speed it can just reduce the wind speed for example if this is a barrier and you have the crops here this is the wind direction now there will be a extent up to which you will have the you might save this this particular area from the wind which was which was prevailing wind but the other other parameters remain same so if there are some areas where wind direction or the wind speed is going to make lot of difference in terms of the evapotranspiration activity that can be influenced so with that we will close this chart here we have looked at all the aspects of the evapotranspiration requirements how we compute those requirements and what are the various methods what are their class points what are their data requirements and if there is any question I can respond.