 Alright, so now we've, you know, hopefully gotten everybody on board with the, with the setup of the problem and the necessary background. And now we can, we can get to the payoff here. So look at some actual attempts to, to estimate the states or remember what we're doing and looking at observations in the magnetic field. And trying to estimate the state of the outer core of the planet, the fluid flow and the magnetic field in the deep interior and use that to make, make forecasts on decadal scales. Alright, so this is something maybe I haven't emphasized yet. The idea of doing this is relatively new compared to a lot of other applications of data assimilation. So it's, it's a people doing data assimilation with the geo dynamo model it's a it's a small young community. So the first proof of concept studies showed up just 14 years ago. And most of these of these three actually two of them just use very simplified one dimensional proxy models of the geo dynamo. And then one use a dynamo model but with just synthetic data experiments. And then shortly after that, you start, you started seeing data assimilation experiments but with simplified versions of the dynamo so models using steady flow in the core and things like that. And then in 2010 that's when you first get prediction of secular variation that the variation of the magnetic field using one of these systems where the dynamic model the assimilation system was a was a full self consistent 3D dynamo model like we we discussed. So, so this was in 2010, and that prediction was actually used you remember I showed the plot earlier from the international geomagnetic reference field. I can't remember if I said at the time. This is something you know they they release these every five years. This includes not just a map of the present field in the recent field but also a projection of the future. Actually it's just what what they what they give there is the average change in the in those spherical harmonic coefficients so average rate of change in the large scale features of the field for the coming five years so you can you can do a linear extrapolation with what they with what they provide. And so, the way it works is there's an international panel of scientists that get together and then people submit their projections or estimates of the recent field, and they they come up with some weighted weighted combination of those those submissions. Okay, so this was just 10 years ago then this was the first time they they use one of these things and included it in the prediction of secular variation. And then since then several groups have popped up around the globe, doing, doing the same sort of thing. I mean, several here is relative as something in the order of 10, maybe groups and in different places that are doing data assimilation with geodynamo models. And so now we've gotten to the point where the most recent IGRF so so this release this is from the most. This is from the most recent release this is their predicted secular variation is the predicted change actually in declination in units of degrees per year for the coming five years. And this includes contributions from several, several of these geomagnetic da systems now. And they do use a variety several of them use dynamo models are also people using other simplified versions of dynamo models or some some physics based models with some simplifications. So you can see you can see actually in this in this map right here you know it's not, you know, it's not a negligible amount of change over five years for example done. Our friends in South America can expect, you know, over the next five years to see something like a degree change in declination. So it's something you could, if you were careful in the right conditions you could you could measure yourself. All right, so here's, here's our first depiction of one of these forecasts. So the NASA system as I said before is an ensemble common filter based system. They call it the the geomagnetic ensemble modeling system or gems NASA really likes acronyms. On the top here. This what I'm showing the top row is just observations so this is for back from 2010 to 2015 you have the the average radial component of the field over that time and this is down at the court so this is downward continued to the core manual boundary. The average change in intensity and units of nano Tesla per year over that same period of time. Right and then down on the bottom, you have the forecasts produced by produced by gems for these these values. And one thing I haven't said yet when we've been looking at these plots of the field down to the core manual boundary, which you can you can see here is that. Of course you see it's still largely you see the signal of the dipole field, right the field coming out in one hemisphere and back in and the other but you can see down at the core manual boundary. You actually have these reverse flux patches here in the southern end of South America and off the southern coast of Africa. And you don't you don't see these at the surface of course but you see, you do see the South Atlantic anomaly in this region here. All right, to give you a better picture of what this is doing over time. I'll show you assimilations from the system. This is going to be a video I'll start here in a second. And what this is going to show you is actually the the observed magnetic field. Over the last while the radial component of the magnetic field over the last 400 years, and then the forecasts of the radial component, as it assimilates these observations, and it's doing assimilations every every 20 years. So, that's why on the right and the forecaster one you'll see you see this periodic jerking then in the forecast as it assimilates observations to keep it on on track. And this is also, this is also with the, this is with the dipole contribution removed here. Okay, so that's why you don't you don't see that if we just showed the dipole and we can seal a lot of these these finer scale features that are in the, and the observations in the forecast so that's just taken out for the sake of clarity. So, as I said they're, they're now several other da system using these dynamo models, and allow them to use in ks. Just recently so you can cast for example I'll talk about this actually this system a little bit more in a bit. This one has been described in a couple of papers by Serena Sanchez. And then recently, for the first time, a hybrid variational scheme was used. This is a group in in Japan. And in fact, both of these systems are also these these are two of the contributors to the to the recent IGF release. Okay, so some of the contributions to to the IGF forecasts that don't use geo dynamo models, maybe they use physics based models. Some of them use just actually mathematical methods just for to do some some extrapolation. The, you know, they can they can work fairly well what makes doing the dynamo assimilations interesting now is that is that you get estimates of of all these physical features of the dynamo that otherwise go on observe so for example you get these estimates of the core flow and the magnetic field in the interior. And so this is actually a nice picture from the Sabrina Sanchez paper, where they're showing the after their last assimilation before they did their forecast in 2020. You see the instantaneous variation in the intensity of the radial component in the field that's what the coloring is. And then these, these vectors are the core flow the horizontal for flow at the surface of the core mantle boundary. And the shading indicates the velocity so it goes from the light light shades it says are five kilometers a year up to 40 kilometers a year for these these dark one. And so that's pretty typical it's not something on the order of like 10 kilometers of year a year as a typical velocity in the fluid of the outer core. Okay, and so you can see, you have this this pretty complicated looking flow pattern at the core mantle boundary. And, you know, you can say well that's, that's great but you know you just spent all this time telling me that you know all this, all of the system goes unobserved so how do you even know how do you evaluate this how do you know how well you're doing. And you've really got a couple of ways to get a grasp on on how well you're doing predicting these these unobserved features like the core flow. The first one is of course observing system simulation experiments so I know this has been mentioned a couple of times or last week and a half but just as a reminder, right the idea would be that I could take, I could take my dynamo model. Run it for a while. Record that run. And then take the things that I can actually observe like the magnetic field, and maybe add a little noise to those and then try and use my assimilation system to reconstruct the model run, I just did. And then I have a true quote true velocity field and things like that compare with. And so a lot of the, a lot of the experiments. I've experienced with these assimilation systems over the last 10 years have for obvious reasons involved doing these observing system simulation experiments. And then of course the the ultimate, the ultimate way to evaluate how well you're doing or to suggest how well you might be doing it at estimating these unobserved quantities is to just look at your success in forecasting future changes. And so, the observing system simulation experiments have have shown that given enough enough data and the right conditions, you are getting, you are getting much improved estimates of the core flow particularly the boundary but also over time. And so the core mantle boundary even tens of kilometers into the, into the outer core. And then, and then forecasts show improvement with the, with the assimilation of these magnetic field observations. And in fact, continue to show, continue to show improvement up to the present day as well as we get more and more observations available the magnetic field. The forecasts are getting better I'll talk about that in a bit. One of the nice things then about having this dynamic model and this estimate of the whole state of the system is that you can go ahead and, and run it forward and try and make a projection, further than say five years out like the IGF models. And this is, again from that Sabrina Sanchez paper they, they went ahead and made their, their predictions for the secular variation over five years and then went ahead and ran their model out 50 years into the future to, to 2070. So up here at the top this is just a depiction of their estimate of the, of the geomagnetic poles in blue and the dip holes here in red so the geomagnetic pole that it's just, if you approximate the field by by a dipole versus with the dip holes this is this would just be where they predict the field will be vertical at the surface of the earth. So down here, this is their prediction for the South Atlantic anomaly so of course from 1970 up until 2020 you're looking at observations and then from there forward that's their, their prediction. And so something I didn't mention earlier, but one of the changes that's seen been seen in the magnetic field for a while is there's a general westward drift the structure of the field. So you see things like the South Atlantic anomaly slowly drifting, drifting the west over time. And so in their projections they, they predict that to, to continue, and actually this the coloring here indicates the intensity with the with the darker purple and lower intensity level so they're predicting and this is in general agreement with other projections like this that that the South Atlantic anomaly is going to continue to drift west and and weaken further. Okay, so this is some of the results we're getting up, but as I said, this is a, this is a relatively new application of data assimilation. And it's a relatively small community of people working on it. And so there are still a lot of a lot of challenges that have to be addressed. And so I want to just go over what what some of those are, and maybe the way we're, we're thinking about how to deal with them. So of course, as we've already said, you know, we, this is a very sparsely observed system, you just have these spherical harmonics describing the magnetic field near the core mantle boundary. You know, I alluded to this earlier when you use the sequential assimilation systems like the ENKF system and NASA or the system that the group with Sabrina Sanchez is using. What you see is that the forecasts at the present day improve. If you go back, even hundreds of years in the past and start assimilating observations. So we could do with more data. The problem is when you look into the past. Of course, the temporal and spatial resolution of the data isn't as good as the last two decades where we have satellite based measurements. Okay, so to illustrate that point. This video shows the radio magnetic field observations of the radio magnetic field over the last 2000 years. And of course, far back in time you only have those low degree spherical harmonics you can only reconstruct what the large scale field looks like. So if you look down or up the top of the video, it's counting up I don't know if people could see it, but you'll see when this reaches 1600 will get into the historical record. And suddenly you'll see, there it is the increase in increase in resolution. And so what I'm what I'm getting at here is that we know it seems already that we know with the systems that are already in place now. We would be able to do better with our forecast and estimates the state. If we just had 100 years of satellite based observations right because this is a, this is a dynamically a slow system compared to say something like the weather. So, when you use one of these sequential assimilation systems like an ENKF, typically you have a so called spin up period, right and so this, this plot over here is an illustration, actually not from a geo dynamo model but a proxy for the chemical dynamo that we used to to investigate some issues related to geomagnetic DA, but the important thing is this these are forecast errors using an ENKF for synthetic data experiment over time, as you do more and more simulations. So what what I'm saying is with with the real model and the real observations, we're stuck right now we're still somewhere on this on this error curve where we're headed down with our forecast errors. So you so with the ensemble assimilation system. The idea is you keep assimilating observations and your collection of simulations sort of hones in over time on the true state of the system, and we just don't have enough high resolution data, going far enough in time, possibly to really to really fully spin this thing up spin the filter up and do it as good as we possibly can estimating the state and making forecasts. So that's one issue. I think that these geo dynamo models are are run in parameter regimes that really don't match those of the earth. And so you have systematic biases in the in the forecasts. So I'll talk about the magnetic Ross be number really quick, and the the equipment number. Okay, so these are just these these are just non dimensional parameters that represent the ratio of the magnetic effects to rotation effects in the case of the magnetic Ross be number or in the actual number case fluid viscosity relative to rotation effects. So different simulations, for example, used by the dynamo model at NASA, these are on the order of 10 to the negative six. In reality, the earth actually is is much different. In particular, you see this, the equipment number here is off by something like nine orders of magnitude. So this, this is usually the point at which people that aren't familiar with this problem, you know spit out their coffee and choke a little because this, this looks pretty. I mean this this looks like a huge problem and it is a problem but I'll explain in a second why you can get away with getting interesting results, regardless. So the reason for this is just purely computational. This is probably a problem that that a lot of other people on this in this talk have in their own in their own models, right you just you simply can't you can't resolve things when you use these these parameter values not with the computational processes you have right so the spatial and temporal resolution right are going to be proportional these parameters. If you try and bring down the equipment number right to lower values you're really, you're really effectively making viscosity fluid viscosity very small. You start getting a lot of a lot of turbulence and find scale features in the flow that becomes really difficult to resolve. And we're just, we're just not there yet with these dynamo models. All right. The reason that the reasons you can still get some interesting results though is that even in these parameter regimes, these dynamo models make magnetic fields that that look like the earth and a lot of important ways. I like to use the phrase earth like some people some people really don't like that phrase, but but you see a lot and in discussion of this topic. And so this is the, this is a figure from the paper people always point to in this discussion this paper. And what it's showing is these these different shape symbols are just dynamo simulations with different eckman numbers. And then the horizontal axis is actually another parameter called the magnetic eckman number and the vertical axis is a magnetic Reynolds number. The point is that the shading tries to tell you something about how, how earth like the simulation is in terms of, you know, does it have a dipole dominated field and, and what sort of time scales does that field vary on compared to the rest of the field. Okay, so there's anywhere there's been a there's been a fair amount of work done in identifying places in the parameter space where you get stuff where you have a nice dipole dominated field like the earth. And it varies in similar ways as as as the earth, but there's still this still has some major issues right so you have this non dimensional model of the geo dynamo. How do you have any of these observations you want to assimilate into it. How do you relate things in your model to to the observations right what's for example what's a time step in your in your model now you know what's one year in your model. You don't know you have to you have to make some sort of choice. And it varies a lot depending on what kinds of parameters you pick so this is just a collection of dynamo simulations using different magnetic Ross be numbers. And on the vertical axis you have the typical timescale of the dipole timescale of variations in the dipole, and on the horizontal axis you have the typical dipole intensity. And these are these are log scales here so you know you change the magnetic Ross be number you get different different timescales variations in the dipole very different intensities. You have to make some choice about what your, you know what your time step actually represents in geophysical time if you're going to assimilate observations, they have to decide how to scale magnetic field intensity to assimilate your observations. And so so this is an area where it's it's still not quite clear with the, with the optimal choices are. And that these, even with these generous parameter values. The models as I said before are still are still very expensive. So, this is this plots trying to show the number of floating point operations you need for a simulation over single magnetic free decay time. And this is and this is as a function of the inverse magnetic Ross be number so so here's where we're at now. And the main thing to get out of this is if you move over to an earth like value. You're increasing the number of floating point operations are increasing increasing your computational expense by a factor of four or not a factor for four orders of magnitude. So, you know, we're just again are just not close to being able to simulate in the true parameter regime of the earth. The consequence of this when it comes to running data assimilation particular ensemble based data assimilation is that the ensemble sizes you can run with are limited. Right, you'd like to run an ensemble based DA system you'd ideally like to run as many as many simultaneous simulations as possible. But for the most part people run, run these systems with only a few hundred ensemble members, but the dimension of the state space. So the length of that vector x that describes the full state of the of the dynamo model is typically typically in the millions. Okay. And so what that means is that you end up with a lot of sampling air when you go to compute the statistics from the ensemble. Right so this goes back to the discussion of the ensemble common filter algorithm, right you take your ensemble and you and you look at how things are correlated in your, in your forecast. Now that few ensemble members compared to the dimension of the state space by random chance. Almost almost certainly you're going to end up saying that that two parts of the state space are correlated just by accident by sampling here when in fact they, they shouldn't be. Okay. And so so this is a major issue. Fortunately, this is something that I think probably other people who do things like numerical weather prediction with ensemble algorithms are familiar with. And they've found the numerical weather prediction people, you know, have some some good ways of dealing with this. And a big one is called localization. So the idea of localization is you you want to knock out these spurious correlations that might pop up because you're using a small ensemble. And for example, covariance localization you would accomplish this by by taking your ensemble covariance right from your simulations that P, and then multiplying it element wise multiplying each of those covariances by some fixed factor between between zero and one. And that's usually done in a in a spatial context. Right so the idea would would be for example, I showed a illustrate a Gaussian decay of correlations centered on on me right now out here in Southern California. And the idea would be if I had some, if you have a weather model, right, and you have covariance between temperature, say down here in San Diego where I am, and just up the coastline in Los Angeles. You would let correlations that show up in your song ensemble between those two variables stick around you would multiply by a factor of one or maybe point nine or something that. And if I'm well across the border and in the Mexico down here and looking at temperature, and my ensemble tells me that it's highly correlated with with temperature up here in in San Diego. You might not want to trust that you might think that that's just a, that's just a sampling error, and because these things are far apart they shouldn't be instantaneously correlated in that way. Right, so that's usually the motivation for localization and that's, I mean that's where it gets its name from localization. You only allow parts of the state to interact locally. But the issue is that's not going to work for us so this is the reason that I've emphasized in the first half of the talk that the observations of the magnetic field, and the description of the state are all in spherical harmonics. Right, so this this covariance here for us this P as telling us about correlations between spherical harmonic coefficients. And so they don't have a particular location in space associated with them. There's not really a measure of a physical distance between them. So there's this question of how do we identify in this problem with the geo dynamo spurious correlations. You know, another way this sampling error stuff is dealt with, not the issue of spurious correlations, but an issue where you start underestimating uncertainty, because you have a small ensemble right you might. The ensemble members might start to become very close together and you come over confident and you're in your forecasts. You know, you don't have enough ensemble members going to really give you an idea of the level of variability in your estimates. And so people use techniques called inflation a lot of times to deal with that issue and that's, that's not a, that's not really a problem here you don't need some measure of length or a notion of distance to do this this is a lot of times this is just like right before you do an assimilation you take your ensemble members, and you push them away from the mean a little bit by a by a certain factor. Okay, so this, this is a big unknown and how to do something like localization, and only recently have some people started to really think about these things. So in particular. So the Sabrina Sanchez group has started doing something like this so this is, if you can't tell I really like this, this 2020 paper of theirs it's really nice and has, it has a lot of nice figures in it so I've borrowed a lot of those. So what they did is, they went and computed they they made a really long run of their dynamo model. And then they looked at the long term correlations in that run. And that's what they're showing us here so this is actually on the horizontal axis, these are coefficients for the political magnetic field at the core mental boundary. On the horizontal axis you have a coefficients, describing the poloidal velocity field the flow of the fluid. And these are the long term or you might call them climatological correlations in the system. Okay, and so certainly for a lot of these. So there's this color scale here that gives you what the what the correlations are and so white is zero CC a lot of these over a long time are uncorrelated. So there's this clear structure in here. And in fact they they zoom in and show us it's what they describe as a checkerboard pattern. Right. And so they decided to go ahead and use some different variations on this, this checkerboard pattern so they're showing what their localization matrix might look like here. So the idea is it's just made up of ones and ones and zeros right so for for spherical harmonics that seem to be correlated over long runs. When you're doing the assimilations, and your ensemble indicates a correlation there, you go ahead and just leave it intact don't mess with it. And so the variation pops up in your ensemble for between two spherical harmonics that don't seem to be correlated over a long run, then you zero it out. Okay. And then over here on the right, I'm just showing from their, from their paper the experiments they did with different ensemble sizes and different variations on this localization scheme. And this is just the uncertainty in their forecast, and the error in their forecast and so the main point is they, they were able to get the same sort of results at a reduced ensemble size when they when they employed this sort of localization scheme. And as I said these models are expensive it's a big, it's a big deal because now they can run. They can run more assimilation experiments. I also think also just like this plot here because I think it's neat you can see, they're assimilating from observations from sometime back in the 1800s up till present day. And you can see, I think they're they're doing this every five years in here they're assimilating observations. And then you can see when you get to the satellite era, and they start assimilating observations every year, and you can see this this sudden drop right here so you can sort of see that, you know, we can be envious of people in 100 years that have, that have a century worth of satellite observations because you know who knows where this curve will will be by then if you assimilate all this stuff. Unfortunately, one of the issues with exploring techniques for localization inflation is that what you'd like to do is just run a bunch of experiments with the system to see what works well. But as I've already said, these things are really expensive, and I'm sure that this was no small task I don't know exactly what kind of computing resources they have but I'm sure this these experiments on their own. Are not something that they just did the matter of days I'm sure I'm sure it took a while. So, in other applications of data assimilation. People have used proxy models you might call them to prototype strategies assimilation strategies for the problems like localization and inflation. And in fact, I mentioned before these first proof of concept studies from 14 years involved really simple 1D models that were supposed to reflect some of the properties of the dynamo problem and assimilating observations of the dynamo. These are these are fairly simple models that don't exhibit chaotic behavior though and the dynamo is is a very chaotic system. And then recently we developed a proxy model that's two dimensional and you have a chaotic flow and 2D that's coupled to a 2D magnetic field through that induction equation. And turn the magnetic field influences the velocity field through the Lorenz force. And both the magnetic field and the velocity field are described then by a by a scalar. That's actually what's in the coloring in the video. And so then the ideas, just like with the observations of the dynamo, we can describe the state of this model. We can do a scalar field and so for example on the surface of sphere, we can describe the state of the model using spherical harmonics, and then we can, we can do synthetic data experiments where we see how well can we reconstruct this 2D flow. If we only know about large scale spherical harmonics describing the magnetic field. Okay, and so that that lets us go ahead and run a bunch of numeric we can run thousands of numerical experiments seven that system because it's much simpler computationally than the dynamo but of course I mean you're giving up a lot of a lot of stuff by doing that. We can run a bunch of experiments. And for example, this is a collection of forecast error plots needs synthetic data experiments as a function of ensemble size for various ensemble common filters where we've we've modified them different localization inflation schemes and you can see a variety of responses to the implementation of those schemes. The important thing though is that it let us run a large ensemble a large enough ensemble that you can be confident in the ensemble statistics that you're getting right you can run an ensemble that's, that's larger than the much larger than the dimension of the system. Right. And so, actually what I'm showing down here is in this proxy model a correlation coefficient in the forecast ensemble over time between two modes that climatologically are are uncorrelated. So over the course of a long run. The two modes are completely uncorrelated, but that's not the case in the forecast ensemble the really large forecast ensemble. And it turns out that's because over the short term if you start looking at correlations between these modes over the over the short term forecasts. The forecast error can be correlated right you have a collection of ensemble members that starts from a very similar state. And then the energy can be shared between these different modes these different spherical harmonics in complicated ways. And so you get a really complicated correlation structure for the short term forecast that doesn't doesn't necessarily show up. So what I'm getting at is, for example, if you look back at the dynamo model correlations. One of the issues we may be having is that you look at the climatological correlations and you you want to zero out some of these correlations some of these covariances in here in your forecast ensemble. And you can be correlated climatologically, but that may not actually be what you want to do it may be that the short term forecasts that you're using in the assimilation system. These, these things should be should be correlated. All right, so now I just want to sort of wrap up what we just talked about, and maybe describe sort of where I think things might be headed or some of the some of the directions that things are heading in. So what we talked about was the so called main magnetic field or the core field of the planet, right and that's the field generated the convective flow in the outer core of the geo dynamo. And we had this issue, or we have this issue right where the magnetic field measurements reflect the influence of a lot of different sources, not just the geo dynamo that we're interested in. And because of that, we, we had to rely on these geo magnetic field models, people build from the observations that describe a potential for the field in spherical harmonics we had to do this spherical harmonic business, right to isolate the large scale features of the field that we believe are coming from the geo dynamo. And this is actually just an illustration I didn't get a chance to include on earlier slides. This is the observed field up at the top. In 2015, the coloring is the intensity, and you have some level curves around that South Atlantic anomaly. And again this is another illustration of when you when you downward continue this to the core mantle boundary. You see a much more, a much more complicated structure you can see the same contour lines here for the South Atlantic anomaly. So let's get, get much more messy. And then as we just discussed this whole issue of doing things in spherical harmonics is important because we're limited to small ensemble sizes from the computational expense of the system. And normally you might fall back on something like localization. In fact, that's something that in large systems with ensemble common filters. It's generally agreed on that you need to do something like this if you if you're using small ensembles. But the spherical harmonics make that a real challenge is still not clear exactly how to do that so how to control for spurious correlations popping up in our, our forecast ensemble. And then the other issue that we talked about is that the parameters and these dynamo models just aren't right. They don't, they don't match the parameter values for the earth and so we have a systematic biases and in the forecast, and it's also not certain what the optimal way is to rescale things to match the observations. So, going forward with these ensemble based assimilation systems. We're going to have to keep finding ways to keep the necessary ensemble size low. Trying to find ways to do localization like the Sabrina Sanchez's group is done. You know, you can, you can say that well, well, you know, hopefully we'll get more computing power, and then maybe can run a bigger ensemble. But because these issues with the parameters. You know you'd also like to if you get more computing power you'd also like to push the dynamo models closer to the true parameter values of the earth. Even if we get more computing power right you want to give it you want to give it back right away by increasing the resolution of your of your dynamo. Probably a lot more experiments need to be run to understand how how we're scaling these things. As I said it's just because of the expense these systems it's it's difficult to do all of the experiments that you might want to do to the best possible scalings for for forecasts. And I think there's also this question of, are there approaches, you know spend a lot of time here describing how you do all the stuff in spherical harmonics to isolate the signal the dynamo but you know are there. Are there other ways to go about this or are there other things that could baby be modeled so that it's okay to assimilate direct observations of the magnetic field instead of doing a spherical harmonic stuff you know if you could do that then it would, it would let you do things like localization more easily. I you know in there I think there there's some people actively thinking about this. You know it's also possible one thing that's been in the discussion since this first started a little over 10 years ago is what other observations besides the magnetic field might be used to constrain the the geo dynamo system. And one of them is is decadal scale length of day variations it's it's known that decadal scale changes in length of day are are associated with changes in the fluid flow and the rotational the angular momentum of the outer core. And so there's this idea that could you use that to somehow constrain the fluid flow and similarly decadal scale changes in in decadal scale polar motion has also been seen to be correlated with changes in the angular momentum in the outer core. So the issue with both of these things is that it's still this would be some sort of integral over the over the core this this observation right represents a cumulative effect and so, you know just like with the magnetic observations, this sort of global, in a sense there would be associated with a particular location in space. And then the other thing I just I want to mention as I focused here on on simulations with geo dynamo models, but in terms of producing forecasts. Either there are other possibilities in particular. So this model discussed in this Baron zone paper from 2020 and in fact this was another contributor to the IGF release that just happened, and they use a statistical model. And they model a variety of sources not just the geo dynamo but but the other sources that we talked about some corrupting the signal or showing up in a magnetic field measurements. And so because they go ahead and model those things. They assimilate, they go ahead and assimilate raw observations into the end of their model so they don't have to do this this business with the spherical harmonics and that seems like it could be a pretty a pretty promising thing. And I think with that, I'm out of time and I'm at the end here so I'll stop. Thank you very much.