 America's. Today we have our lecturer, he's, as I mentioned earlier, he's an early career scientist and who affiliated to the Scream Institute of Oceanography from the background, he's a mathematician and made a master degree in applied mathematics as and he's dealing with the numerical analysis modeling the data simulation, particularly in geomagnetism. People will hear they say his progress together with his colleagues in area of data simulation in geomagnetism. Please, now it's your time to start the lecture. Thank you. All right, thanks. So, see, am I, can you see my screen? Yes. Okay. Perfect. All right. Yeah, so, so thanks for that. And, and thanks everybody for coming. Thanks to the, to the organizers. I've enjoyed, as you said at the beginning, good morning to everyone over here in the States. I've enjoyed the last week and a half. Unfortunately, I, you know, a lot of these, the early sessions are in the middle of the night for me, but the, these sessions at the end of the day are at about eight o'clock in the morning out here. So I've, I've enjoyed the last week and a half getting up every day and starting with a cup of coffee and one of these nice talks. So I'm, I'm, I'm sad that this is almost over, but it's been, it's been a lot of fun, a lot of interesting stuff. So I, I want to start out by just saying a little bit about some of the other people that I've, I've worked with on this stuff. So, as Alec said, I'm going to talk about geomagnetism in particular and data assimilation. And so this is just something I've had an interest in for, for a few years now. But really it's Waysha Kwong and Andy Tangborn that have been working on this for a long time for over 10 years now. Waysha Kwong is out at NASA Goddard Space Flight Center. That's out near Washington DC. And Andy Tangborn for a long time, he's now at NOAA, but he was affiliated with UMBC. It's a university that's also out in that area. But also he was working at NASA Goddard Space Flight Center as well. And they are there nice enough to invite myself and my advisor, Matias Morsefeld, to, to come on board with them and start thinking about these things that I'm going to, I'm going to talk about today. All right. So this is roughly how it's going to go, or hopefully how it's going to go. I want to start out by explaining, you know, exactly what I mean by the, by the title of this talk, predicting secular variation in the magnetic field and with data assimilation. So we'll start out by getting on the same page and, and making clear what, what part of the magnetic field we're actually interested in and, and why we care about it. And then from there, we'll be able to talk about the observations we have the magnetic field that are going to be relevant and the numerical models. And then from there, we'll be able to actually get into some results and some, some of the challenges that we see in this work. Okay. So the magnetic field that we're interested in is sometimes called the core magnetic field or the main magnetic field. This is the field that's generated in the outer core of the planet. So this is this nice illustration from the European Space Agency. And so you see the solid inner core of the planet. And then the liquid outer core. Right. So this starts about 3000 kilometers below the surface of the earth below our feet. And it's made up of mostly iron and some nickel. But the important thing is that it's convecting. It's undergoing turbulent convection. And it's electrically conducting. Okay. So this is what generates the typically dipole dominated field that they're trying to illustrate here. Right. So this is the field that makes your compass point point roughly towards the geographic poles, but certainly not exactly. Right. The field protects protects the earth and the surrounding area from, from the wind. So you have charged particles that come off of the sun or also from, from outside the solar system cosmic rays. And, and this radiation tends to get trapped by the magnetic field of the earth. And oftentimes it's directed towards the magnetic poles. And that's actually what's responsible for, for the auroras. I don't know if we have any people that are at latitudes where they're, they're able to see those. I've never seen them in person myself. So over here on this plot in the upper right, this is a map of the magnetic field intensity at the surface of the planet. And I think back in, I think from 2008 sometime within the last, last 20 years. Don't worry about the white dots for now and talk about that second. So I said this is a dipole dominated field. That's, you know, why it's been able to be used in the past for things like navigation. But you could see from this picture that it's not, it's certainly not a perfect dipole. You don't have something that's just symmetric about the equator. You know, as there's these interesting features there, you see the red spots here where there's a high intensity near the poles. And that is because of the dipole. There's a lot of flux there. But then you also see, you know, these sort of lobes of intensity. And then maybe the feature that stands out the most here is you have this blue spot in the middle of this intensity map that's at the low end of the intensity spectrum here. So the red is about 70,000 nanotesla. And blue is something like 20,000 nanotesla. Right. And you can see that that's actually about half of the intensity of the field at equivalent latitudes elsewhere. The green is about 40,000 nanotesla. So this blue region is usually called the South Atlantic anomaly, this weak spot in the field. The white spots, what those are, are actually locations where a particular satellite, the Topex satellite, I think it was measuring something with oceanography. I can't remember sea surface height, something like that. But the white spots are where that satellite experienced instrumentation failure, had trouble with its electronics. And you can see pretty clearly that those failures are clustered around the South Atlantic anomaly. And this is because you have this weak spot in the field, and things like the solar wind penetrate further into the overall field, they get closer to the earth. And it's much easier for that to start interfering with electronics on board satellites. And this isn't an issue that was unique to this Topex satellite. This is a persistent problem with instruments on satellites. They pass through the South Atlantic anomaly, and they're much more prone to having issues and sometimes very serious issues. They've had catastrophic failures of electronic systems on board satellites, so they've been permanently damaged by the radiation out there. And then people also, you know, it's something that's often repeated this, this, I say, you know, the field protects the earth from the solar wind. Sometimes you'll hear people talk about it protecting the atmosphere of the planet. There's been this thought for a long time that the solar wind, in the absence of a magnetic field would strip away the atmosphere of the planet. And so a magnetic field maybe is necessary for a planet to be habitable. And people point to Mars as an example of a planet where it once had a magnetic field like the earth, and it's since died out. And of course now much of the atmosphere has been stripped away. It's a very thin atmosphere in Mars. That's something that's a little more recently some people have objected to the idea and say maybe it's not the, maybe it's not the case. But that's something you'll hear people say sometimes. But of course, a classic, the classic application or use of the magnetic field that we're probably all familiar with is in navigation and surveying. And so this is, this image shows a declination of the field at present. This is from the IGRF. It's an international geomagnetic reference field. So they release this every five years, a map of the current state of the magnetic field. And the declination is just how far off from geographic north, say your compass would be. So out here in California where I am, my compass would be about 10 degrees off, say from here north. All right. So this magnetic field that I've shown you these pictures of it, and it's got some of these interesting features like the South Atlantic anomaly. The deal is that changes over time. It changes on a variety of different timescales. So on decadal timescales, you get some changes in the morphology of the field, the weak spots and strong spots sort of grow and move. And for example, the magnetic poles move around. And sometimes this is something you'll see in the news. Sometimes we'll talk about, oh, the magnetic north pole moved you know, 30 kilometers over the last year. And this is actually an illustration from data over the last 400 years of the northern pole as it moves around. This is an illustration from NOAA. Actually, the speaker at the end of the day yesterday was from NOAA. So this is a, I have to apologize, this is a U.S. government agency. So of course the picture here is centered on North America. But I promise that most of this will take a more global perspective of the field. And on longer timescales, the field undergoes these really dramatic changes where the polarity of the field can completely reverse. Okay. So the northern magnetic pole, the southern magnetic pole switch, right? This has happened several times throughout Earth's history. This down here is actually an illustration of what's called the virtual axial dipole moment. I don't want to get caught up in the details of what that is, but just think of it as roughly a representation of how strong the dipole field is at a given time. And this is that intensity, the dipole intensity over the last 2 million years with present day at the right and 2 million years ago at the left. And then the sign indicates the polarity. Okay. So you can see, for example, in this plot that back here at about 780,000 years ago, we had the most recent reversal. And actually we had a handful of these in the last 2 million years. And roughly over the last something like 20 million years, we've averaged one of these every 250,000 years or so. So it's not an uncommon thing in the history of the year. All right. So what is it we're actually going to try and do here? What's going to be the point of this work? So there are two main objectives. We're interested in estimating the dynamic state of this geodynamo system. So that means not just the magnetic field and what it looks like, but also the fluid flow and the outer core. So this is an image from a simulation, actually, of a dynamo model at NASA. And on the left here, they're showing a single magnetic field line from their model. And on the right, this is a streamline for a flow in the inside of the outer core. So the red sphere in here is the solid inner core. And the outer sphere is just not the surface of the earth. This is just the outer core of the planet, the fluid here. And so I show this now just to make it clear that while we see this nice dipole dominated field out here towards the surface and from observations up in space, you can see the magnetic field down in the outer core, at least according to simulations. It's actually very, very messy. And similarly, the fluid flow in the outer core is very turbulent. And so we'd like to get an estimate of the state of the system. And then you'd like to be able to, as I said, the field changes, you'd like to be able to use that information to make forecasts of how the field's going to change on decadal scales. You'd like to project where the field looks like 5, 10, 50 years into the future. And so I'll show some results on that later. This is just a little teaser right here. This is from a recently produced forecast from the system at NASA. It shows the field intensity, the projected field intensity in 2025. And you have some contour lines here for that southed land only. And so these are the main goals. There are many other reasons to be interested in this, but I think this is the easiest way to frame this, estimate the state of the geodynamo and try and produce good forecasts of the magnetic field going forward. And to achieve those things, we'll look into using data assimilation. All right. So now we're on the same page, hopefully. And we can talk a little bit about exactly what observations are available to us and what sort of numerical models we have. And then I'll just briefly review the aspects of data assimilation that we need to have just for the discussion of this problem. Okay. So I just showed you a bunch of figures about the current state of the magnetic field and the magnetic field even in the distant past, the reversals that's undergone. But how do I know all this stuff? So the observations actually come from a variety of different sources. Certainly in modern times, you have satellite-based observations of the magnetic field. So this in the upper right is an illustration from ESA of SWARM. It's a collection of three satellites that have magnetometers on them and measure the magnetic field on the planet. And there have been a couple other missions similar to this over the last two decades that have done the same thing. So for a couple of decades now, we've had satellite-based measurements of the magnetic field. And of course, there have also been, since the mid-1800s, there have been terrestrial-based observation stations. But then to learn about the field before those days, people have come up with a lot of creative ways to get an idea of what the past field looked like. So in terms of those reversals in the distant past, we know about those things from the paleomagnetic reconstructions, like paleomagnetism people. They go and look at magnetic material and igneous rocks. They look at rocks that have cooled down slowly over time in the past and frozen in the signal of the magnetic field. So they do things like this is an illustration of mid-ocean ridge where you have this upwelling magma. And then it comes to the surface, the ocean floor, and it slowly cools off and the seafloor spreads out. And as it cools off, the ferromagnetic material in there sort of freezes in the signal of the magnetic field. So this illustration is just showing from something like the five million years in the past, say, up till the present, and the colored regions represent areas where you'd have present day magnetic polarity and white, the reverse, right? So you get from these mid-ocean ridges as you go out sort of a recording of the polarity of the dynamo. And so people will go out with boats and drag magnetometers behind the boat and read this barcode signal of the history of the polarity of the dynamo. And this is all, I'm making it all sound really simple. This is a whole complicated inverse problem on its own that people make whole careers out of. It's not as easy as I'm making it sound. People have done other really creative things. There's archaeomagnetic reconstructions where they've gone back and looked at, for example, material in pottery and bricks and things like that over the last few thousand years to get an idea of what the field looked like. And then for the last few hundred years, they've even gone back and looked at ship sailing logs. Somebody's meticulously gone through compass-recorded compass readings from ship sailing logs over the last 400 years. And that's actually how we know some of what we know about that South Atlantic anomaly and that it's been around for at least a few hundred years. Okay, now if you just take, in the present day, if you go and you just take a measurement of the magnetic field, if I sit here with the magnetometer and I measure the field or you have a swarm satellites in orbit and they measure the magnetic field, you of course measure a lot more than just the field of the geodynamo. As I'm sure a lot of people here know better than I do, there are a number of magnetic sources on this planet other than the other than the outer core. And so this illustration from the ESA highlights some of those. So this on the right here is a cross-section of the planet. And so you have down here the solid intercore and the fluid core that's the geodynamo in red. And that's what we're going to be interested in here. But of course you also have currents in the mantle and currents out in the ocean, the ionosphere and up in the magnetosphere. And all of these things are influencing any measurement you make. And so what they show on the left here tries to illustrate the various contributions from these different sources. Okay, so this is on the vertical axis, the magnetic field strength and each of these oval shapes represents a different source. So this narrow red one here is labeled long-term dynamo process. So that's what we're really interested in. And on the horizontal axis, don't worry about this description on the bottom right now, just focus on this. This is spatial wavelength. So this is really just about the size of the feature that you're looking at. Okay, so this is on a log scale. These these axes are both on a log scale here. So over here are large on the left hand side are large length scale features. And so over here, this long-term dynamo processes, that's almost two orders of magnitude larger than the next strongest source. So the point is, is really big features of the magnetic field. That's almost exclusively when you make a measurement, the signal of the of the geo dynamo. So this is why over here, this is, for example, the dipole over here, this large length scale feature, the big dipole dominated field we see. This is why you're able to use this. This is why you can, you know, with just a compass, you could you can see the signal of the dipole, because it's this large length skill features are very dominant over these other sources. But when you start getting into small magnetic anomalies, small scale magnetic anomalies of say a hundred kilometers, a few hundred kilometers or less, then it's things are starting to get messy. A lot of other things can be influencing that. Okay, so I should say there's going to be, you know, there will be a couple of equations along the way here. And I put them up for people that are interested in these things. But I think, you know, we'll be able to have a largely conceptual discussion about the issues that are of interest here and avoid getting bogged down in any details. So, but this is going to be important understanding the problem. So what happens when they take these measurements of the magnetic field from a satellite or a terrestrial observation station say is you typically assume that where you've taken the measurement, you're in a source free region, you're in a region without without any currents. Okay, and when that's the case, then the observed magnetic field B here can actually just be defined as by a potential field. It can be defined as the gradient of some scalar field. If you do that, you can actually describe this scalar field, this potential V, in terms of what are called spherical harmonics. So if you're not familiar with spherical harmonics, that's fine. I'll tell you just basically what you need to know. If you're familiar with Fourier series, it's the same idea but on the surface of a sphere say. The idea is just that you break down the scalar function into pieces in the component parts. So for example, I have this illustration down here at the bottom on the right hand side. If I had this function on the surface of a sphere here, the scalar function on the right, I could break this down. I could describe this in spherical harmonics as the sum of this function. So this P here is just, it's called the associated Legendre polynomial. So it's just some function of theta of the meridional angle on the sphere. So this could just be written as the sum of this function and this function. So you just have these coefficients here that are called Gauss coefficients, G and H, and they just tell you how much of each of these ingredients you need to these little functions you need to add together to get the scalar function you're interested in. So this is going to be, this is just going to be an important component of this problem and I'll explain why on the next slide. So basically the idea is you describe the magnetic field not by just saying at this point it's pointing in this direction with this intensity. You actually have a potential that defines it and you describe that potential as a list of these Gauss coefficients, a list of how much of each ingredient you need to make the field in terms of spherical harmonics. Okay, so why do they do this? It goes back to the plot about the contribution of different sources that I showed a couple of slides ago. So it's widely believed that the large scale features as I showed in that plot are really the signal of the geo-diamol and I should say this index L here in that formula I was showing for the spherical harmonics that really corresponds to length scale. So the lower that L is the bigger the feature is you're talking about. So for example that G, L equals 1, M equals 0 here, that coefficient actually is what gives you the dipole, that's the dipole ingredient. The bigger that coefficient G, 1, 0, the bigger, the stronger dipole is. As you move to larger values of L you get the finer scale features. And so the stuff up to degree 14 that's believed to be the dynamo. So the point of all this is by describing the field that we observe in this way it helps you isolate the signal of the dynamo. And I should say these other stuff here we don't need to worry about it but A is just that's the radius of the surface of the earth and then R is going to be just where you're at the distance from the center of the earth. So once you have a description of the magnetic field that looks like this from your observations of the surface under certain assumptions you can downward continue that. You can take your measurements of the surface and get an idea of what the field looks like down at the boundary of the geodynamo. So down near the core male boundary. And so that's what this video is showing right here. So you have the radial component of the field at the surface. And you see this largely this dipole dominated field you know in the tens of thousands of nano tesla range. And then when you use this setup and you downward continue it look at it what does the field look like at the core mantle boundary. You get intensities that are about an order of magnitude higher. And you also see that all these sort of fine scale features here are less smoothed out now you see a lot more a lot more activity a lot more stuff going on that you can't see out of the surface. So you know I go to the trouble of explaining all this because it's actually these low degree spherical harmonics it's the spherical harmonics that are actually used in assimilation systems these are things that actually assimilate into models of the geodynamo to try and estimate the state of the magnetic field in the core flow and in the interior. Okay. And so this is an important aspect of this problem because assimilating these spherical harmonics actually causes it causes a lot of issues there are a lot of issues associated with this. All right. So I told you about the observations and what sort of models do we have available to us. So I don't think we're going to have a chance to really get into this but I thought it was worth mentioning that there are there are these simple low dimensional models that try and recreate the behavior of the dipole over time and this is a simulation from one of them. So the idea here is this is just supposed to look like that plot I showed earlier of the previous two million years where you see the intensity of the dipole varies for a while and then you get these reversals where it changes polarity that's what this is assimilating. There are big 3D numerical models of the dynamo system that simulate the fluid flow and the outer core and it's coupling to the magnetic field and those have been around since the mid 90s. The very first one was built by Gary Glatzmeier and this is actually a snapshot of one of his models. These are the magnetic field lines and again like the simulation I showed earlier from the NASA model you can see that away from the magnetic field you get your nice dipole dominated field but down near the in the outer core near the core mantle boundary the lines get all twisted it's very messy and in fact this these snapshots right here are showing this simulation undergoing one of these reversals. So actually if you run these models in the right parameter regime and you run them for long enough you'll you'll get this this sort of reversing behavior out of them you can see these sorts of things here. This is another thing I don't think we'll really need to talk about but I think it's so interesting that it's worth mentioning people usually find this interesting. There have been multiple attempts to simulate this sort of system in a laboratory and there are several labs around the world that have done this I shouldn't say several but maybe something like on the order of 10 or something like that. The one I'm most familiar with is out at the University of Maryland so that's near Washington DC and the labs run by this physicist Dan Lathrop and this is a picture of their system so this is actually this steel drum here is is three meters in diameter it's not a small thing and then inside of this they have a they have another sphere that's supposed to be like the inner core of the planet and they can rotate the outer and inner sphere at different rates and then they fill this thing with liquid sodium and they start spinning around and they apply a magnetic field to it and they watch how the field lines get all contorted and everything and amplified by the by the flow inside and it's actually you know if you don't know liquid sodium is can be pretty it can be pretty dangerous stuff it's you know reacts violently with water and things so they have to I just went to a talk recently actually given by by by Dan Lathrop where he talked about they wanted to they wanted to make some modifications to the interior of this experiment and so disassembling it all and and cleaning it out and and storing the liquid sodium all as it is a very precarious process that's pretty serious about safety there but it's an interesting thing but anyway we'll focus on these these numerical dynamo models so let me tell you a little bit about about those and again this will be this will be a place where I have a few equations but we don't need to we don't really need to get bogged down and then I just like to point out a few things and discuss discuss them conceptually okay so there are different ways to to simulate this but a pretty typical way away the the dynamo model at nasa works is it relies on on on these three equations so this top equation here is just a usual navier stokes equation okay for the for the fluid flow v and the outer core with some rotation effects so the rotation of the planet is a is a critical piece of the generation of the magnetic field and then it's it's driven by by buoyancy so you have some density perturbation controlled by this equation so that you get so that you get buoyancy you get upwelling inside of the dynamo that's then twisted around by it by the rotation complicated ways but the main modification if if you're not familiar with you would call this magneto hydrodynamics or mhd right so the the physics of when you have a fluid like this moving around that's electrically conducting basically to to oversimplify it you just have a typical fluid flow but with the addition of a lorence force term that's what this is this j here is just the current density in the fluid so you have a usual fluid flow in the outer core but you you also have a lorence force so so the magnetic field is able to influence the fluid flow in the outer core one thing i'll come back to later is that these these models are are pretty computationally expensive they're not simple things um i want to say a few more things about the the middle equation here that that governs the the evolution of the magnetic field the so-called induction equation this is something that actually just falls out of under certain scalings falls out of out of maxwell's equations and really what you have here is just induction you have that you have the fluid this conducting fluid that moves around in the magnetic field and so you you induce new magnetic fields i mean then you also have some some decay of the magnetic field some transfer of magnetic energy to to kinematic right and so that's actually this this video over here on the right what's being illustrated here is over the course of the simulation the net energy change from uh kinematic to magnetic that's in yellow and then conversely the conversion of of magnetic energy by biomic dissipation okay and uh so so the point of showing this is just again you can see you can see you have a pretty complicated pattern in the outer core of magnetic field generation and and decay uh the other thing we're going to need to understand about this is that when you when you do one of these dynamo models you typically decompose the magnetic field into two scalar fields so this would be called a toroidal and poloidal decomposition and the only thing you need to know here uh is that you do this with the models and then you describe these scalars in those spherical harmonics so you describe them the same way that i discussed describing the the observations and then it's actually the spherical harmonics that describe this scalar field here p that that we have the observations of that's that's what we're going to assembly and the other aspects of the field the other aspects of the of the dynamo model so the fluid flow and the outer core and then density perturbations are similarly described in spherical harmonics so so the thing to take away from all this uh that's going to be important is you know we have a description of the state of the geo dynamo and a description of some observations the magnetic field from the geo dynamo and all of those things are described by spherical harmonic coefficients so they're not they're not described by saying this is what the direction and intensity of the field is at a certain point or this is what the velocity looks like it's it's described in this in this spectral way and this is as i said before this is going to be important because it it it causes some issues and doing the assimilations okay so we have these we have these observations of the magnetic field uh but there's a lot of things we can't observe like the fluid flow or the magnetic field in the interior we have numerical models of the system we have these numerical geo dynamo models and so obviously a natural thing to do then is to try and merge these things through through data assimilation okay so this uh this is going to be a brief review i guess of data assimilation i'm not going to spend too much time on it because i know we've already we've already seen this a couple of times this week i just want to use it to again highlight uh an important part of this problem so let's just say that x represents the state of the system and y my observations right so x is the state of the geo dynamo and y is is this collection of observations of the magnetic field uh you know in the usual way you assume that these these are related by by some observation operator and that there there's some noise you don't have perfect measurements in the system and of course the whole goal as we've as we've seen in discussed this week then in data assimilation is really to describe the the posterior distribution here the distribution of the of the true state conditioned on on your observations and so what i want to emphasize uh again is that in this problem that x here the the description of the state is a collection of spherical harmonic coefficients it's it's not explicit descriptions of the velocity or magnetic field directly and similarly this y here as those those observations in the form of spherical harmonic coefficients so this whole distribution is a distribution over collections of spherical harmonic coefficients and then a lot of the of the currently operational geomagnetic da systems um use ensemble based methods including the the one at at nasa that i'll i'll spend some time talking about so uh i think this is this is going to be the last the last bit of of equations here that we need and again we won't get bogged down and i might just want to focus on a few conceptual things uh so as a reminder with ensemble based da like an ensemble common filter that's that's going to be what the the nasa system uses the idea right is that you have an ensemble of of simulations you're running simultaneously of multiple instances the model so in this case multiple instances of the geodynamic model and here i have a little cartoon of this setup right so you have some observed states and some unobserved states and simulations correspond to a particular color right so there's a there's a blue simulation and a yellow and a green and a purple here right and so you run you run your simulations or collection of some simulations your ensemble up until the time where you have some information in this case these observations in the magnetic field so it would be like this red dot here with some associated uncertainty indicated by these these error bars and then you use your your preferred scheme da scheme right to to adjust your estimate of both the observed and the unobserved state right and the important thing in the ensemble based simulations is that the way you decide how much to adjust your unobserved state right based on the the state you do have observations of is is by the ensemble statistics so you compute the covariance of your ensemble you look at how how say in this cartoon example how at this time is the observed state correlated to the unobserved state according your ensemble right and then you make your adjustment to the observed state and and the unobserved one right so so this this would be like in our problem the equivalent of i have this observation of magnetic field but i don't know what the fluid flow and the outer core looks like so how do i how do i adjust the fluid flow according to according to what i see in the magnetic field okay and so this again when we don't need to get we don't really need to to talk about this i know we've talked about we've seen the colman filter at least a couple of times or last last week and a half so this is just the particular methodology that's used but the important thing here is really just that we're going to come back to is this issue of getting statistics from from the ensemble to see how things are correlated okay and so as i said a lot of these the nasa system and several other geomagnetic da systems like it are currently using ensemble colman filters and as i said we're we're going to come back to this i'll just say right now to to foreshadow what the what the issue is realize as i said several times this this x here it's a collection of spherical harmonic coefficients right so this ensemble covariance is a collection of covariances between spherical harmonic coefficients it's telling you how these coefficients are correlated and so that that creates some some interesting problems all right i think that's probably a natural we take a break at 45 minutes so that's probably a natural place to go ahead and do that if that's okay absolutely that's okay fine okay it's perfect yeah thank you then it's able to reconvene and 555 perfect the local time